Thing one to keep in mind. The use of a boat declines proportionally to it's distance from you. You think you'll be the exception, but you won't. Now partly this does depend on your use. Do you have weeks or months at a time or is most of it weekends? If the former, perhaps. If the latter, no way.
I have to correct a couple of pieces of information. Insurance doesn't require a captain, but they do look at experience. If you're already insured, that's not likely an issue. However, you may well have to change insurance carriers to get the right insurance for the coast and then your experience comes into play. As to hurricanes, there are more boats in Florida than any other state and they don't all leave for hurricanes, so know that you can get insured and you can find some reasonable protection or care.
Currently I'm guessing your drive is about 45 minutes to an hour. I'm going to toss another idea your way, in the opposite direction. The Tennessee River. Chattanooga is a two hour drive for you. Wonderful area. Good marinas, great cruising and the distances you're looking for. You have the perfect boat for the Tennessee River. I'd really consider it strongly.
As to checks on the boat, alarms are a good start, but I'd also engage someone locally to check regularly, unless I found a place to keep my boat in dry storage. It can be a management company, a marina that provides the service, or even a liveaboard you befriend. The other thing I'd do is cameras. That way you can visually check and be alerted to problems.
Someone asked why not Georgia. I love Savannah, but it doesn't make your drive that much better. Still it cuts off some time, so I'd consider the Georgia coast. Don't get mislead though as the Marinas are quite a bit beyond Savannah. Thunderbolt is a nice area for keeping a boat. Then there's St. Simons, Jekyll, and all the other islands. You might even look at Charleston. Even if you're able to save one or two hours of your drive, you've improved the situation. Obviously climate changes slightly too though so there is an offset.
Still, my personal choice from Atlanta would be the Tennessee River. Second would be something in the Savannah area.