As far as I can find (and I hope I am not repeating what has already been said), the last substantive discussion was in 2009 by Ross in the "Bologna" thread, concerning only the Chariot and defending its Bolognese placement as first (viewtopic.php?p=4147#p4147). Since then his only change has been to attribute that placement to Florence first, which then changed the placement of the Chariot twice, moving it above the virtues, and next exchanged its position with the Wheel of Fortune, one way or the other; Bologna, meanwhile, kept the Chariot in its original position.
In this post I want to suggest a third alternative, namely, that the Chariot was earlier above the virtues, as seen in the Florentine lists, but that the earlier placement of the virtues was as in Bologna. In other words, the Rosenwald order, on a sheet probably of Perugia and surely not earlier than 1501 (see Pratesi at http://pratesitranslations.blogspot.com ... rugia.html), may have been before either.
The Rosenwald is at http://trionfi.com/0/j/d/rosenwald/.
The Beaux Arts and Rothschild are at, respectively, http://www.tarothistory.com/images/encyclopedia1.jpg
The three sheets are estimated to have been produced around the same time.
The Florentine orders of that time are presented by Depaulis at https://www.academia.edu/30193559/Early ... 07_p_39_50, pp. 42-44.
Between them the 12 cards of the Beaux Arts and Rothschild sheets include at least 11 of the last 12 cards of the traditional Bolognese sequence. That suggests to me that probably the 12th card on these sheets, the Chariot, was also among the last 12 at that time. This is not certain, to be sure; the two sheets do not divide up so that the last 6 are on one sheet and the previous 6 are on the other. Yet there is still the suggestion, and a reason for supposing that the Chariot is among the last 12, and so probably 10th or 11th.
In that case the two Bolognese sheets for the rest, each with 6 cards (4 sheets of 6), would have been much like the Rosenwald's one sheet (3 rows of 8), with three spaces free to put in three non-triumphs (the Rosenwald has Queens).
What the Rosenwald has uniquely in common with the Bolognese order is: (1) the virtues are in the order Temperance, Justice, Fortitude; (2) there are clearly two papal and two imperial figures, all together between the Bagat and Amore. In both respects the order does not correspond to any in Florence, all of which show the virtues in the order Temperance, Fortitude, Justice, none having or mentioning a Popess card or with numbering indicating its presence - although it still may have been present but unnumbered, as when numbers were put on the cards in Bologna. The difference from Bologna for cards II-V, of course, is that they form a distinct hierarchy, with II and III distinctly feminine. The Rosenwald is most likely from Perugia. If points 1 and 2 are true of both Bologna and Perugia, the Rosenwald's existence is another reason for supposing that the position of the Chariot card in Bologna then would have been above the virtues, by similarity among similars, which again does not yield proof, just a consideration in favor of that direction.
The order in Bologna would have changed sometime after the Beaux Arts/Rothschild lists, moving the Chariot from above the virtues to immediately below.
That it would have changed in that way is not implausible. There is the precedent of Florence, regardless of whether there was a Popess there. The Chariot is before Ruota in the Strambotto, and after Ruota in the handwritten numbers on the Charles VI and in Minchiate. That is only by one position, but in Bologna the virtues, when they are all together, could have been considered a single unit. In the Rosenwald, the Chariot must be before Ruota (as Depaulis concludes), since all the numbers up to X, Chariot, are taken, even though on the sheet Ruota is placed 13th. In Bologna it could have been either before or after Ruota, but since it is still before Ruota in its traditional order later, probably it always was. That would put it in the same position as it is in the Rosenwald.
Moreover, in every early region of the tarot the order did vary in one or two small ways from one list to another, in the 16th century. There is no reason for Bologna to be an exception, except the conservatism of the players, if it went back that far. It seems to me that we cannot infer from post-1507 (or 1513) conditions what was the case before then. At some point at least, some Bolognese seem to have been convinced that Bologna invented the game. If so, they naturally would have held onto the order as they remembered it.
The next question then is, why would the game have made such a change, moving the Chariot card below the virtues, unlike any other known A order? It seems to me that the sequence was meant to convey a moral message, not only in itself but when applied in the trick-taking game (Ross uses a similar argument, but deduces the opposite conclusion from mine). When Temperance takes a trick with Love in it, that means that Love, the crazy kind instilled by Cupid, is properly ruled by Temperance: Temperance is superior to Love. In the other A orders, that is all there is to it. But in Bologna, after the fall of the Bentivoglio and the imposition of a stronger role of the papacy, the Chariot, that is, the triumphator, might have been seen as having to be ruled by Temperance, too. We might recall the Bolognese tarocchi appropriati poem about Imre Tekeli, the Hungarian nationalist of the late 17th century:
Here the ardor is not the passion for the opposite sex, as shown on the Love card, but that of the Charioteer....Tempra l’ardir, trattien il Carro, e ratto
Lascia d’Amor d’Imper la voglia acerba,
...Temper your ardor, slow your Chariot, and quickly
Leave off the immature desire of Love of Rule,...
The title of the card in Bologna, "Tempra", is a verb that would apply to both Love and Chariot. In the old Italian, Treccani tells us (https://www.treccani.it/vocabolario/temprare/), temprare meant both "moderate", nowadays taken by the verb temperare, and a process in treating metals that had its analogy in living, namely that of "quenching", cooling a metal down after first reheating it, often by plunging it in cold water. We might recall that an alternative way of depicting the virtue of Temperance in the Middle Ages was a lady with a vessel in one hand and a flaming torch/cornucopia in the other. It is possible that the "Alessandro Sforza" stag-rider card has a torch (with a lewd connotation), since the card is damaged in just that area, below the upper cup and above the genitals.
In tempering a metal, the result is a finish that is less brittle than it would be, and in that way able to withstand blows better. By analogy, there is the moral idea that in tempering justice with mercy; a ruler actually increases his longevity in power, attending to particular circumstances as reasons for mercy. For that the Chariot should be before both virtues, as being ruled by Temperance. I take this as a reason for changing the order, to deepen the moral lesson. The triumphal Charioteer, being human like the Lover and those before him, is subject to the virtues. Those after the virtues - Fortune, Time, Death, etc. - are not (the Hanged Man is a special case, as Judas was associated with the number 12, for the 12th disciple, or conceivably 13, for the 13th seat at the Last Supper and King Arthur's table).
If the change was in the opposite direction, from before the virtues to after, that change could also be rationalized, by saying that the virtues are part of the education of a prince, and so of anybody, before he can be a good triumphator. However this rationalization is less in keeping with an educational function for the trick-taking aspect, in which subjects that should rule in humans are more powerful than those that sometimes in fact rule, overpowering the virtues. (The Devil is not an exception, because he should rule over the wicked after death. The other powers stronger than humanity are also part of the divine plan.)
Then there is the question of why the order of Fortitude and Justice would have been switched, even before such a change in the position of the Chariot, and even if that order is attested in a few sources (Ambrose Commentary on Luke, V, 62 and Wisdom of Solomon 8:7). In those sources, that Justice is before Fortitude seems merely incidental, whereas the sources in the other direction (Justice after Fortitude) offer good reasons for their choice, as well as being more authoritative (Plato, Aquinas). So the justification for going from Temperance-Fortitude-Justice to Temperance-Justice-Fortitude is much weaker than the other way around. Again it is the Rosenwald order that seems the earlier, although now shared by Bologna rather than Florence.
It is also true that the Rosenwald designs are simpler than those of the hand-painted cards of the Charles VI and of Minchiate. This is not necessarily due to the nature of the medium, woodcuts vs. painting, because the Beaux Arts/Rothschild designs are as complex as their hand-painted equivalents elsewhere. The simpler designs of the Rosenwald, instead of being earlier, could be due to less skill or effort on the part of the cutter, further removed from the allegories in what, despite the primitiveness of the order, is surely a later product than what we have, or perhaps have (since the provenance of those cards is still contested), from Florence.
Backwater places, e.g. Piedmont, sometimes preserve orders superseded elsewhere. So perhaps, apart from the hierarchy of dignitaries, the Rosenwald represents the earliest of the various known A orders, retained by Bologna as well as Perugia even in the early 16th century. If so, that is a good reason for assuming that this order also obtained in Florence, so that in fact there were four dignitaries rather than three at some point (as Depaulis asserts, without argument, in Tarot Revele, 2013).
Moreover, there is some slight reason for thinking that this order would have existed in Bologna before it went to Florence, because, given the general conservatism of players, a change in the order (here I am talking about the virtues) is more likely between cities, a change at the beginning in the second city, than in the same city.
Needless to say, there is much that is speculative here.