Some Ortigia B&Bs are within the ZTL and have dedicated parking so that you can enter the ZTL and park closer to the middle, rather than the giant parking structure on the outskirts of Ortigia.

I could be repeating myself, but thank you the the valuable information about parking and the information on
noto and places to stay in Syracuse. I will definitely check these. We'll be dropping the car in Ragusa and taking a cab to catch the ferry at Pozzallo. The train arrives at 9:05, and the ferry leaves at 9:15 so we wouldn't have enough time.