The only state park I've ever been to was Bahia-Honda state park and its DEFINITELY not beachcat friendly. They made my buddy in his 18SX launch from the little marina and try and sail out the 20' wide channel, and then to get to the ocean you have to be able to sail through the old rail bridge which has nasty currents and is known to be a haven for bullsharks (if that kind of thing bothers you) :P

Upside is that we acutally made it in and out a couple times, and the camping there is spectacular with some very beautiful beaches and good facilities.

There are tons of little put-in places, mostly adjacent to the bridges, where you can put in.