Itinerary question

For the best use of time, I'd suggest you go Venice, Florence, Cinque Terre, Rome.

If you fly out of Rome FCO, you can schedule an outgoing flight around 10:00-12:00 a.m. directly back to the U.S. All of the 6:00-8:00 flights will take you to another European gateway airport where you'll sit around until mid-day to fly out. No reason to get up at 3:00 a.m., as it's difficult enough taking a 10 hour flight without proper rest. And of you fly out of Venice, you'll also be sitting around another European airport.

I'd have gone Venice>Florence>Cinque Terre>Rome as well BUT I would not just cancel any of your hotel reservations until you've been able to successfully reschedule Cinque Terre and Florence. It's not 'early' at all for the CT - hotels tend to book up quite some time in advance - and you probably don't want to risk having to find a new property if your current booking can't shift your dates.

Yes, the distinction between the two routes is not very big. The rail route via Milan is only about 45 minutes extra to say, Monterosso, but only requires one connection and can be cheaper than the route through Florence, which requires 2 connections. Go that way and you won't feel like you are backtracking. So if you are booked, leave it.

The Venice Florence CT Rome might be better because breaks up the trip from Venice to CT which is otherwise a very long loop around the Appenines mountain range. However, as Sam mentioned, if you are already booked, I wouldn't change it. The train from Venice to CT, is not a straight shot, it is a long day on the train, but if done via Milan, although even longer, requires fewer train changes than via Florence. You might want to consider that route.
The advantage of your itinerary sequence is that your last leg (Florence to Rome) will be super fast.

Thank you all for this helpful advice! I think I'll keep my original itinerary...

You're going to have a marvelous time. :O)