Make sure you are going in season (December through April), otherwise you’ll still see a few, but you’ll miss the peak experience. You’ll definitely want to do a tour, I’m guessing you won’t have good interactions without that.
For a less popular Florida attraction, you could try Sanibel Island on the Gulf side of Florida (basically Ft Meyers). We did a similar trip a few years ago, went on a random airboat tour through the Florida swamps, that ended up being a good experience as well.
The whole state is full of great/affordable AirBnBs - can’t go wrong with FL…even if you have to do the worst place on earth (Disney).