OK, thanks everyone. This has been a worthwhile discussion for me in that it's firmed up a couple of things, e.g. a train stop in Padua might work, in Verona it might not. And I think I'll turn my "2 nights in CT, then 1 in Genoa" into 3 nights somewhere between the two, maybe Rapallo. At least that's one less move. I'll leave Parma as a possible day trip.

bilboburgler, your response gave me a chuckle. Fear not: I have spent a week crawling all over Florence. I feel like I've got a reasonable handle on it, hence the plan to see the surrounding areas next time.

Thanks all - now on to the hard part of this trip: Spain!