[JohnN]

Think about zamia - coontie palms. They're very tropical, like a sago palm without the trunk.
There's a grove of 'em in front of the Lighthouse Grill at Lake Sumter Landing.
They're actually a cycad, a "dinosuar" fossil at 250 million years old, it's a native Florida plant and quite hardy when established.

I've read in a few places they can grow from 3'x3' (shorter than what you want) to 6' high, so I'm not sure on the height, but it's a beautiful, slow growing shrub.
Anyway, that's my choice at the moment.
Let us know what you choose. I'm looking for something just like you are.