A couple of thoughts.
First - if you do decide that Ft. DeSoto Park looks good don't be put off by lack of available sites. On Friday mornings (at least this was true before COVID) they release a number of sites for the following week. We were able to get a site that way sort of last minute a couple years back.
Second, there is an RV park in the Bradenton area,
Frog Creek, that my cousin spends the winter at. She's really into kayaking, and she loves this park for that. I haven't been there, and I don't know if there are manatees, but apparently it's ideal for kayaking.
Have fun!
-Speak