You have the Club Carlson credit card that currently gives second night free. There is a Radisson Blu in Rome. I'd research that hotel and see if it suits. If it does, I'd book a room there; perhaps even a premium room given that the second night will be free. That gives you back $550 to use elsewhere.
I agree with others that it is a brutal travel schedule. I'd at least cut Munich and stay in Venice longer, or go to Venice via Florence.