In my opinion the "4 papi"-phenomenon developed from ideas to transfer chess-king and chess-queen (also card king and card-queen) to Trionfi-card-emperor and Trionfi-card-empress.
This idea had consequences for the other chess figures, which also had to be "promoted". For the bishop figure it's known, that it was originally an elephant
with the expression "alfin", in the Cessolis tradition it became the old or elder or the counciller
, in a Slavic variant it has been an archer
. The French name is fou
and the German modern name is Läufer
(runner), associating indirectly an idea of connection to the "messenger-pawn", which had some similarity to the Pagat. Nonetheless a very early bishop
figure is known from 12th century from Northern Europe, so it existed, probably also for Italy.
The Hofämterspiel is said to have been produced 1455 in Bohemia for the young king Ladislaus, who had been 1452 (12-years-old) in Italy (beside other cities: in Ferrara) and with some guarantee he had seen Italian Trionfi cards of this time.
In his game 6 court cards are used, 4 of them are placed on numbers:
Ace = 1 = 4x Fools
6 = 4x Jungfrauwe
9 = 4x Marshall = Unter
10 = 4x Hofmeister = Ober
unnumbered = 4x King
unnumbered = 4x Queen
Although Ladislaus had seen Italian cards, it seems, that his painter wasn't impressed. No Trionfi cards. Instead the deck seems to have relations to the deck of Johannes of Rheinfelden, which knew 5 of 6 court cards in a 4x15 deck: Ober and Unter, Maid = Jungfrauwe, Queen + King ... for the moment we don't know, how the Aces were used - we're still waiting for a translation of the Johannes-of-Rheinfelden text.
But ... considering the French "fou"-expression for the chess bishop and the fact, that Emperor Charles IV had been educated at a French court (so had have French influences), we may translate the game of Ladislaus to ...
Card-King = Chess-King
Card-Queen = Chess-Queen
Card-Fool = Chess-Bishop alias CHESS-FOU
Card-Marshall = Chess-Knight
Card-Hofmeister = Chess-Rook
Jungfrauwe .... ??? ... = PAWNS
If we look at the Cary-Yale and its reconstruction, we see, that Filippo Maria filled the pawns-positions with Virtues, and all "female virtues" were probably all Jungfrauwe = "virgins" and the 7 virtues accompany the bride on her triumphal march, which probably also was a virgin.
Beside that the Hofämterspiel has enough professions to fulfill the usual Cessolis-expectation, that the pawns are professions.
So we have 3 Trionfi card decks (Trionfi interpreted as "Trionfi-function") surviving with Chess relations (all rather different and it was the enjoyment of high standing persons to have different decks) ...
made for 16-year-old Bianca Maria
made for 15-years old King Ladislaus
1463 Charles VI
made for 14-years old Lorenzo de Medici
... and beside that we've an assumed, not really existing "Trionfi-deck" - so a fiction, of the citizens of Bologna with their clear interest of "liberty" of ca. 1440 with 22 cards - , which is said to have caused all that, what followed ... but all these humble persons in reigning positions didn't dare to extend the number of trumps, this was "too risky" ... what shall one conclude about the reality of the Bologna-early-deck fiction?
High nobility had an interest to educate their children to the game, which was officially accepted as "educative worthwhile" and this game was chess. There we have the motif for Trionfi cards and the reason, why Trionfi cards were allowed and other card games not.
A number of 21 special cards would have associated the game with dice and there are 21 points on a die, which were variously attacked and forbidden strongly. It simply wasn't their interest at specific times, when card prohibition still was strong, to have this association.
Well, the 4 Papi developed from chess, when the bishop needed to be promoted, cause Chess-king became Trionfi-card-Emperor (and the promotion caused bishop to Pope and the question, what to do with the second bishop ... so it's not really possible to fix the appearance of the 4-Papi-rules to the years 1438-1441) and if this fails, the suggestion "Bologna deck in 1438-1441" drops back to Marchione Burdochi, and where his decks came from, you say "from Bologna" and I assume "from Sagramoro", but even if "from Bologna" would be true, nowhere is an indication, that it had 22 special cards.
Recently I discovered to my own astonishment in the "The Precipice" - thread, that the Precipice appears on 6 of the 14 Bembo cards and that they've (in numbers, they appear at the only imagined Bembo numbers 0=11, 1, 6, 10, 12, 13 ) some parallels to the Hofämterspiel (which uses 1, 6, 9, 10, ,  for court cards) ...
wrote:Which to my own astonishment meets somehow (not completely) with the structure of the Hofämterspiel, which has court cards at
6 Jungfrauwe (virgins)
(9) Marshalls (... in the Bembo cards no cliff)
11 (unnumbered in the original) Queens
12 (unnumbered in the original) Kings
Whatever it means, this is a little strange ... the discrepancy between both decks might have been caused by adapting the idea to a deck with less (or more cards), one system using 9-12 (4x12) and the other 10-13 (5x14) for something special (at one side court cards, at the other cliffs)
King Ladislaus, for whom the Hofämterspiel was made, was with Emperor Fredrick in Italy, 1452, 12 years old. He should have met Galeazzo Maria at Mantova, 8 years old ... .-)
This led to the idea, that the precipice was used by the designer to part the 14 cards for unknown reasons
in 2 groups, one with 6 and the other with 8. The group of 6 seems to indicate "6 risky actions or states", the group of 8 looks like "8 safe elements".
The "6 risky elements" might refer to 6 different chess figures, as there are king, queen, bishops, knights, rooks, pawns:
Fortune ... Queen
Magician ... King
Love ... pawn, as always
Fool ... might present a weak knight, but also fou = bishop has some logic
hanging man .. hanging from high = rook, tower
death ... an archer = archers were used as bishops, but might be knight
The "8 safe elements" might refer to 8 chess officers (without considering pawns):
Papessa = bishop
Empress = Queen
Emperor = King
Pope = bishop
Chariot = knight
Hermit = knight (or rook?)
Justice = Rook (or knight? with sword? with knight in background?)
Judgment = Rook
Although the 14 Bembo cards appear as the tradition, which brought up Tarot-Trionfi decks with a dominating hierarchical row (1-14 first), it also shows elements of the chess pattern.
So we have a fourth chess deck, following the Precipice detail, now to add to the other 3.
What do we have in the background of all these Trionfi documents up to the mid 1460's? We have real surviving cards and the connected decks have similarity to chess. The analyses of the findings lead to different variations, they show chess interpretations with different opinions, how to interprete the figures ... and all of them have only 14 or 16 special cards. We learn, that there was a discussion and the discussion led to different productions.
You're much too early with all your suspicions about mass productions here and there and variation A doing this and variation B doing that. And you've no evidence of mass-production for the early time.
And if we find a 22 version before or around this time, I would assume, that it would use different motifs.
One detail is interesting ... Justice in the Bembo version has a knight in the background, and so it looks like a knight figure. However, in Ferrara instead Justice was made (later) a very high trump (Nr.20), likely, cause it had been earlier a ROOK (my opinion at least).
The rook in the running chess versions of the time had a very strong position, the chess queen and chess bishop were earlier relative weak figures. So we have as the probable rooks in the Cary-Yale the figures FAME and JUDGMENT-ANGEL, which later in the Florentine deck Minchiate were the two highest trumps. As probably rooks in the Charles VI we've JUDGMENT and the TOWER (and in the Minchiate the Tower is the highest of the first 15 - before the break, when the 20 special Minchiate motifs are imported).
In the version of the Sola-Busca - with a production year of 1491 in far distance to this very early discussion - we have a Tower=Rook symbol at card 20:
... still second highest trump.
And for the Boiardo (I arrange it in a quote, that it is better seen)
In the Boiardo poem we have in Nr. 19
"Tempo, che gli homini a la morte sproni,
Nestor servasti, e si pur vinne al fine,
De un viver tal non par che se ragioni.
Time, you that hurry men to death,
You saved Nestor, and if in the end he came to an end,
It seems impossible to think of such a life. "
The keyword seems to be "Time" (= old Nestor), so "Father Time"
and in Nr. 20, which is in one pair with 19 we have:
"Oblivion di termine e confine
Del tutto sei, Elice e Dido a Lethe
Menasti, e famma e tempo hai in toe ruine.
Oblivion, you are the end and boundary
Of all, you took to Lethe Elice and Dido,
And among your ruins you have fame and time. "
Keyword is "Oblivion", "ruins" (as ruine" last word of the tercet) might associate "Tower" and "Rook", but Fame and Time are also mentioned ... Time is, as already recognized, Nr. 19, so "Fame" should associate Nr. 21. Here it is:
"Fortezza d'animo in Lucretia liete
Exequie fece: per purgar sua fama
Se uccise, e all'offensor tese atra rethe,
Dando exempio a chi 'l nome e l'honore ama.
Inner strength made happy the death of
Lucretia: to clean her fame
She killed herself, and she prepared for the offender a dark net,
Giving an example to those who love their own name and honour."
So, somehow, a sort of clear statement at the end of the poem
20. RUINE = TOWER = SAETTA
Tower, twice at Nr. 20, both probably in Ferrara decks and probably 1487 and 1491 ... after the Ferrarese war, which wasn't old history in January 1487.
The proud chess knight Ercole, celebrated by Boiardo's Orlando's poem had learnt, what defeat means in 1487. He became more peaceful and in his later phase rather religious, actually infected by Savonarolism.
The Giovanni festivities in Florence had been stopped in 1478, after the assassination of Lorenzo's brother. It seems, that the whole Italian Trionfi culture took a pause, more or less. At the climax of this development Ferrara lost its feathers, but survived. Ercole's theatre initiative, starting already January 1486 was an operation to restore the old glamour of Ferrara, though on the background, that the economical conditions in Ferrara were still bad.
"Ferrara in ruins", that's the message of the high tower in these new Trionfi games, after the war, which ended in 1484.
A 22-structure was used twice in Ferrara, possibly (?) for the first time. Ferrara was often the initiator of something.
Well, that's later.
From our knowledge we have to assume, that after-1450 Milan preferred a 5x14 version and Ferrara also (70 cards note of 1457), but it should be assumed, that inside the Ferrarese mind was the idea "justice is a rook" and in the Milanese mind "Justice is a knight".
And with this we've 5 different Chess-Tarot versions to observe (Cary-Yale - Charles VI - Hofämterspiel - Bembo Cards - Ferrarese 14-trumps-variation), and if we would have full overview about all productions, we probably would have some more.
Chess is the elder brother of playing cards and still in 15th century unequal mightier than the social phenomenon playing cards. Galeazzo Maria Sforza has a little time with playing cards in 1468-69, but then his gambling interests are occupied with chess and betting on tennis. Meister Ingold has a long chapter about chess, which fills the half book and than a much smaller chapter about playing cards between other gaming occupations. Trotti is ready with Trionfi and card decks in 2-3 sentences at totally 35 pages, they're noted and that's all. On the negative prohibition side playing cards are small against dice. Simply : playing cards were still a small social phenomenon, a not too wide spread object a long time (maybe already of some more importance in Germany). Suitable for women and children, or very young men, at least at the courts.
Alfonso of Aragon left card-playing, when 18 ... this probably meets with the general understanding, when young men should become more serious in their behavior. Cards were for children and young men. Women did need them, as they had educative function with the children - so somehow allowed for women.
Chess, still focused in 15th century and still the king of the games, was improved and radically changed (inventing the moves of modern bishop and Queen) in ca. 1470 in Spain and the common change everywhere took only one generation ... so stated at a chess history page. 1495 it reached Italy, probably with a Spanish pope in 1492 ... I still have to study the details.
Thanks for the Strambotto information ... still there seems to be the (small) possibility, that it didn't happen before 1505 and so all these questions stay alive.