you're relatively new here, so I've to explain a few things.
There is a relative complex "theory-in-development" usually called 5x14-theory.
It took it's start from an observation of the Pierpont-Morgan-Bergamo-deck, which was - as far the trumps are considered - painted by two different painters (one is assumed to have been Bonifacio Bembo, the other is "unknown"). This condition was earlier explained by "some cards were lost and replaced later", with the "5x14-theory" was proposed, that painter Nr. 1 had a commission for a deck with 5x14 cards, and painter Nr. 2 added to the complete deck 6 further trumps - some time later.
With this it was assumed that these 14 trumps plus the 4x14 smaller arcana were a complete deck in the intentions of the designer and of the commissioner.
Generally Tarot History had presented the theory or opinion before, that Tarot had have reached the modern standard form in ca. 1450. As "evidence" served (more or less only) just the Pierpont-Morgan-Bergamo deck, but naturally, with another second explanation like the 5x14-theory, it wouldn't serve this way. It's plausible, that this deck form developed ca. 1452 (there is a letter reporting a Trionfi card production in Cremona in 1452), but with 14 trumps or special cards it would contain another message and meaning as with 22.
In 2003 the domain Trionfi.com was started to research the oldest conditions of playing card development with a special attention to the 5x14-theory. Then three new, former not considered were found, which suggested, that the 5x14-theory was correct and none factual piece of evidence, that a Tarot or Trionfi deck with the standard form existed till the Boiardo poem (which definitely uses this form).
1. A document of 1.1.1441 reports the production of 14 paintings (called "figure") as present for Bianca Maria Visconti, which was then as a guest in Ferrara. The painter was Sagramoro (later Trionfi card painter variously), his objects are also called "figure" later, the commissioner was probably Leonello (who a year later really ordered and paid for Trionfi cards), the date (1st of January) was a date used for gambling and card playing during the Christmas season. A lot of indications exist, which serve in the argumentation, that these 14 objects were playing cards, but a definite declaration, that these objects were Trionfi or playing cards wasn't given.
2. A letter of Jacopo Antonio Marcello about a playing card deck in November 1449 uses "Ludus triumphorum" for a deck with 16 gods as trumps, with birds as suits and totally 60 cards. With this the generally used assumption of the older theory, that "Trionfi cards (or similar expressions)" meant naturally decks with 4x14+22 cards, was contradicted.
3. A production note of 1457 in Ferrara speaks of "70 cards" for each deck (two are produced). 70 cards (instead of 78) are no problem for the 5x14-theory, but it was a problem for the older assumption, that every Trionfi-deck meant a standard Tarot deck with 22 trumps or special cards.
We did a lot of research to get a plausible dating for the Boiardo Tarocchi poem - the first sure appearance of the later deck form, though as a deck rather unusual. The momentary state is, that this poem was likely made for the wedding of Lucrezia d'Este in January 1487 (the Roman Lucrezia is the highest trump in this deck, which has 22 "figures of history" and not the usual 22 motifs).
From this some security developed - though still opposed by many - that the 5x14-theory had taken a well protected position in the discussion.
Naturally ideas developed, how the state of a 5x14-deck developed, which other conditions were there and what happened after ... from 2003 - 2010 is a lot of time. Meanwhile there are seen 2 major developments (A + B):
A. 5x14 deck development ... evidence is ..
1. document 1.1.1441
2. the 4 Bembo trumps in the Pierpont-Morgan-Bergamo deck
3. document with 70 cards from 1457
B. 5x16 deck development or "16 trumps + unknown number of small arcana ... evidence is ..
1. Michelino deck with 16 trumps, described by Martiano da Tortona in ca. 1425
2. Cary-Yale Tarocchi, which has 11 surviving trumps, but could be reconstructed with 16 trumps, assumed to have been made 1441 (with competing other explanations)
3. Charles VI. deck with 16 surviving trumps
In the B development it's seen in the interpretation, that these decks followed Chess ideas ... 2 x 16 figures fill a chess-board and a chess iconography had been already developed since Cessolis. Chess was very popular in the considered time.
In your own analysis ... as you has shown above ... you follow similar lines as we did in our analysis. It's also perceived by us, that Tarot developed from the Imperatori/Karnöffel/Kayser game, it's also perceived, that Petrarca's Trionfi and the group of Virtues (you relate them to Boethius) were important factors.
Actually ... the Imperatori cards, somehow connected to the number "8", likely developed about the Ober and Unter position in a usual card game (which also are 8 cards) as King-King-King-King, Ober-Ober-Ober-Ober and Unter-Unter-Unter-Unter. Kings had to rule in their kingdom (the 4 suits), Ober and Unter (the marshalls) had the profession for military activities, which in a card game would form the "trump-function". Generally some fantasy was spend to illustrate the Ober and Unter, but Kings stayed Kings usually.
This trumping form (Ober and Unter = trumps) is still used in Schafkopf, a game played at the border to old Bohemia (in Bavaria and in the Riesengebirge north of Czechia).
In the relevant early playing card time (later 14th century) Bohemia was the emperor country, from here he ruled the Roman Empire (Charles IV, then later King Wenzel; Sigismondo still was a son of Charles IV). Schafkopf as a name of a card game appeared first in ca. 1700, but the basic rule is very simple and very near to the original iconography (it should be understood, that the original iconography likely influenced the early games more than later games).
The trumping form in the "oldest Tarot cards" (Michelino deck 1425) had 16 trumps, but these seem to be just "extended court cards", as the description speaks only of kings and no other court cards ... so the gods (likely) were court cards and somehow also independent trumps, prdeining the later really independent 5th trump suit, which became in the development Tarot cards.