We stayed at Frog Creek in Palmatto , mostly snow birds but people and facilites were nice
2012 Winnebago Journey 36M Cummins 360
2014 Jeep Cherokee Limited, Air Force One, Blue Ox Avail towbar
249 Campgrounds,55K miles driven in our motorhomes and 1193 nights camping since we retired in July 2009 - 37 States and 29 National Parks
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.
2016 25ft.Ventura Sporttrek
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.
2014 Triple E Regency GT24MB (Murphy Bed) with all the good stuff
Fiat Abarth, fast little car, great gas mileage - hardly know its there
Berkley, the amazing camping cat missed dearly (1996-2012)