Frog Creek in Palmetto would be my first choice. Have stayed there for short stays. It is about 40 minutes from AMI. Not far from Tampa Bay via kayak. Nice folks, dog friendly and like you are camping not resorting.
2007 Toyota Tundra 5.7, Auto 6sd, Prodigy 2 brake control,
Reese dual cam WDH with 1200lb bars.
2008 28ft Dutchman Classic with 20ft slide.
We drove over to the island a couple of times in January when we were in Bradenton. I remember there being 2 or 3 c.g.'s just before the south causeway but I don't know the names, only that one in particular looked very pricey. Google might help or contacting the Chamber of Commerce on the island.
2007 Holiday Rambler Admiral 30 SFS with lots of good stuff!