I think your itinerary is fine. From Florence to Palermo you can flight (check the cheap fares reserving in advance) while from Palermo to Naples you can take a ferry.

The Hotel delle Muse in Rome is really nice, clean and in a quiet, fancy area. Furthermore, the owner (Giorgio) is a Ziner and a friend. He will help you during your stay here.

About the GTG, I am up for it (as always!), just remind me before you come... I am so busy that I can easily forget!

Hope this helps. Ciao Flavio in Rome