I decided to give Project Gotham Racing another chance last night and made an important discovery -- what I thought was a "you can only play this part on XBox-Live" feature, turns out to instead have been the next level of the game. So my belief that you had to keep playing the Florence street race over and over until you beat it on every difficulty before you could go on to the next race, was just me misreading the interface!
So, yeah, nice one, Gneech.
The game turns out to be much more fun when you can go through different levels at a lower difficulty! It could still stand having some cheering bystanders or a passenger cheering you and/or giving you grief, but the actual racing part turns out to be better than I thought.