You've lost me. Ferrara shows evidence (not conclusive, of course) of 13 and 14 trumps early on. In Milan, the Michelino had 16, and 16 trumps would correspond to the CY suit cards, for 5x16. In Florence there could, for all we know, have been 16, or 17 if we take the existence of the Moon and the Sun as weak evidence for the Star, and no evidence or favorable conditions before a little before 1450. There is no evidence for Bologna before 1442, also inconclusive, although conditions were favorable starting in 1438. So why couldn't there be 16 or 17 trumps ca. 1438 in Milan, 14 in Ferrara, same time; and 16 or 17 in Florence ca. 1449 or so? And Bologna the same as Milan, ca. 1439 (homage to Filippo, more plausible than creation from scratch ca. 1438 after a period of severe repression), in a limited way at first, maybe a printed edition 1440 or 1441; then later (c. 1449 or so) Bologna changes the look to be more like Florence, where Sante and his artists come from, one change of several. Since the ruling families of all four cities play cards with one another, the trump sequence could have had the same three sections, but with somewhat different cards, different numbers of cards in each section, and different orders in each, because of different local conditions. All of these cities have their local heroic/tyrannical families, and at least three with betrayals or other persecution (Ferrara is lucky until later). At some point the number of trumps shifts to 20 in Milan, without Devil and Tower; in Florence, without Devil and Popess; in Bologna the number is 20 or 21 (with or without Tower), still similar-looking to Florence except that it has two popes and two emperors, one of each pair looking rather effeminate. Later, in the interest of standardization, Florence and Milan have 21, too, but without Bologna's odd innovation. At some point (before or after standardization) Devil is added. Ferrara at some point--but before the "Steele Sermon," and Boiardo's poem, whenever they were--joins the others. I'm not saying that's the way it was, just that this account is as plausible as any other, and perhaps more reflective of the evidence.But since all the orders use, in various arrangements, the same 22 subjects, this implies that there was an original set in a particular order that would explain both the choice of subjects and their sequence.
Also, 22 is a prima facie strange number of trumps for a deck to start out with. 14 or 16 plus maybe a wild card is more natural, as it corresponds to the number of cards in the suits. (And if 13 wasn't an unlucky number until tarot made it one, there is no necessity, of course, that the Death card be number 13 early on.) 20 is a natural expansion: decades were also natural, as in the number of pip cards; and witness the "Montegna," which most art historians place in the 1450's or 1460's. Two decades make a natural progression of the soul, first down and then up through the ten spheres (Empyrian through Luna). Then in the interest of standardization, one more sphere is added, adding the sublunary to the other ten in each direction. (One might be tempted to say, well, that's a natural sequence, too; but I don't see such sequences of 11 written or pictured at that time.)
Your assumption of Bolognese tarot conservatism 1435-1513 (roughly), based on Florentine conservatism then and Bolognese conservatism later, seems to me unjustified. Later on (after the 1400's), Bologna's tarot was conservative and Florence's wasn't, even though both were type A. So why couldn't Florence have been conservative and Bologna not, 1435-1513? Bologna was subject to frequent radically shifting external political and artistic dependencies then, especially in the critical period 1435-1447, unlike Florence then (either the shorter or longer period) and Bologna post-1512. So the Bolognese may have needed to be occasionally profligate redesigners, to keep up with changing times.So, after all of these choices and weighing of options has been done, all that remains is to choose a sequence and imagery to interpret. In the light of all this and what I have said before about having no reason to think the Bolognese were profligate redesigners of the imagery or sequence, I took BAR as my model, on the premise that whatever changes may have been done in the approximately 60 years between the Ur-Tarot and BAR, they can be measured by the differences between BAR and the painted A types, and the other differences can be explained the different places of origin - BAR in Bologna, the painted cards in Florence. Since Rosenwald (Florence) shows greater similarity to the painted cards (Florence), I assume that BAR would have equal similarity to what a Bolognese deck of the 1450s would look like, and that the difference between the 1450s and the date of invention is utterly inconsequential. Therefore, by this reasoning, the BAR sheet is the closest design to the Ur-Tarot.
I have not disputed this point, that there is contemporary politics in the game. It is my affirmation of it that makes me think that a deck with the "four papi" rule would have been too politically volatile for mass distribution in the period 1438-1440 and also the period 1442-1447. The "four papi" rule would have been offensive to many even in the one town of Bologna; many wouldn't have agreed about there being two popes, even cynically; and some of those that did would have disagreed about the wisdom of a game that said so. Fights might have broken out over this point. Only when the schism ended (i.e. after 1446) could there be a deck with two popes that all could agree on: a Pope in Rome and a Patriarch in Constantinople (and the cynics could still say, to each other, that it was the two popes in the West). That's the only time a mass-distribution deck with the "four papi" makes historical sense in Bologna, although I suppose there could have been a limited trial-run, withdrawn except for export, in 1440-1441.Showing politics, including Popes and Emperors (here wrestling, later bowling or playing cards), as a game was common enough with advent of woodcut, so I don't think it is far-fetched to see it IN a game as well.
Thanks for the explanation of the "two emperors." So unlike Felix and Eugenius, they're not in competition with each other. A possible difficulty is that then the situation with the emperors is not parallel with those popes. The explanation is ad hoc in that way. Eastern/Western is more parallel, with a subtext, for some people, of the two popes of the schism and nothing for the emperors, unless there is some aspect of competition between a bearded and non-bearded emperor relevant to Bologna that we don't know about, e.g. opposing policies. However an ad hoc explanation is better than none.