I would say vincas, a.k.a. periwinkles - beach sunflowers also flower heavily, but periwinkles are more similar to impatiens in form & colors.

I'm a little bit farther north than you, but I understatnd that purple cone flower is supposed to do well, you might look into the florida lantana as well. you're pretty far south, you might take a look at this nursery (Sarasota climate), http://www.floridanativeplants.com/groundcovers.html

I've never ordered there before, but i'm fixing to so ill let you know how it goes. It definitely will have some good ideas for you. They have a ton of beautiful native photos right for your zone/area. i've been looking at their sunshine mimosa as a potential flowering groundcover, its supposed to grow all overt the southeast.

since they are native, they are all low to no care plants once established.