Florida does take a little getting used to. There are some places with paved shoulders but they can be problematic. They often have debris or little breaks in them to keep you on your "toes". Florida does not have an extensive rural road net unlike some other states I have ridden in. So quite a few of the roads have significant traffic. However, there are rural roads with reasonably light traffic volume. You just have to go look for them.
I think your experience was skewed by going to Sanibel. It has only that one road going out to the island and a bunch of tourist traffic. Lots of tourists crowded on a single road is a bad thing no matter where you go. The roads at the coasts tend to have fewer options so you get more crowding.
There is some very nice riding in Florida. You just have to find it.