Well... Aside the fact in 1490's St. peter was like this...
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So far I think the TL is quite good. Some doubts in some point, like the fact Cesare won't use Chambery as his first court for logistic reasons (can help to keep contact with the French but he needs an Italian capital - Turin or Alessandria (the latter the better aside for the auspicious name is in Monferrato, the true base of his power); also, OTL Cesare became yes Duke of Romagna, but in doing that he was forced to subdue the various Roman families across Latium (Orsini, Colonna) to then march towards Marche and for last Romagna. Here we have TTL a situation where Cesare was away many years, I doubt his older brother Giovanni (assuming to be still alive TTL) would have managed to restore order out of Rome. So Alessandro gave as OTL lands which Cesare had to conquer before rule them.
Also... For paradoxal it may be, attempts of rejuvenation of Roman culture in Italy during renaissance age won't bode well. Why? Because Humanist ideals may take input from classical thoughts, but to going over them. Medieval age is more embued with Roman influence respect to modern age - even in regards of art. To make an example, the fact Brunelleschi took inspiration from the Pantheon to create the dome of S.Maria del Fiore, doesn't mean he did a "roman dome"; or if Michelangelo took inspiration from roman sculptures, the David is not at all a classical like sculpture.
Plus what it was said in 1861, "done the Italians there is to make the Italians", is still valid in 1500. Cesare may have some appeal from intellectuals and literate nobles (and in Italy there were many who didn't have the same studies) but to form and unite Italy, the call to Roman heritage has to be built over an Italian foundation, not viceversa. To the majority of the Italians of the time, Rome is just the city of the Pope. They would have scarce knowledge of a Roman Republic than Empire.
Besides, Napoleon's empire was probably the one who took more inspiration from Roman aspects (and we are 300 years later than Cesare) and yet was something of totally different. Same for Mussolini's propaganda, but why sounded better to the Italians of the 1930's? Because they mostly had the opportunity to go school and knew the basics of ancient Roman history.
In substance, this tirade is to state Cesare has to build better the "neo roman" roots of his reign, it may work in front of a King of France or a Holy Roman Emperor, but less in renaissance, and "roman emancipated" Italy of the time.