My wife teaches so we have the freedom to do what you speak of in the summertime. We have yet to set off but I have given it some thoughts. I'll share the biggest sticking points I've come up with.
It takes awhile to really get used to how long it takes to get places in a boat. Couple that with finding marinas close to descent airports for commuting and transportation to the airport and it is going to take some planning. I think you would be fine until you get to about Norfolk. After that there are some really long runs until you get to FL.
With that in mind, if we do it, I have decided we would probably have to stay at least a month at a time in the different marinas that we find. First, monthly rate would be cheaper, especially considering you would probably be staying at the more expensive marinas closer to town and the airport. You could possibly anchor out, but I wouldn't be comfortable leaving my boat unattended on an anchor for four or five days at a time. Second, if we don't stay at a marina for extended periods, I would basically spend all my off days moving the boat and never getting to enjoy the different stops. My wife would but I would be away at work. Third, since we decided to stay longer at each stop, we could drive the car ahead to the marina, then fly back and get the boat and continue so on throughout the trip. Having a car of course would make it much easier to get to work, not to mention the store, especially if the airport is far away from the boat.
Finally, you have to plan for hurricanes. Things would not go well if I was away at work and my wife had to prepare for a hurricane alone. Or for that matter if your boat was left alone while you are at work. And you can't plan on having advance notice for these things either. The first hurricane of this season was a low pressure system that came out of GA. It moved into the Gulf and came back ashore 2-3 days later in LA as a Cat 1. Also, I don't know how all parts of the country are, but some marinas in New Orleans require boats to be either moved or taken out of the water depending of the tropical forecasts, so that is another thing to think about when looking at marinas to leave your boat at.
All in all though, if you can navigate those issues, it would be an incredible way to live. Keep us updated.