Since there are many Florida marinas that have and accept liveaboards, but don't acknowledge this when asked; even if there were a list, it would not likely be accurate. Are you interested in remaining within the Fort Pierce Area? ....Northeast Florida? The Keys? Panhandle? For us, we like to keep our longer stays in Florida marinas at places where we can sail during an afternoon without breaking an inlet,- St. Johns River, Indian River, Biscayne Bay, Keys, Tampa Bay, etc. In addition to location, what are you looking for in costs and amenities? Do you want to be near a metropolitan area, public transport, rural wilderness, schools, shopping
? Also, what size boat, draft
?.... can you pass under the 55' fixed bridges?
I recommend that you present a post on the Liveaboard forum here within the Cruisers Forum with some thoughts of what you desire. There's a great wealth of knowledge here that can serve you well.