Smartersail seems like it would be a good match for you but they are in St. Petersburg.
I see near you the Bluewater Sailing School but they don't seem a good fit for beginners.
The same might be true of Bluewater Miles.
Island Dreamer also seems to be advanced and live aboard.
Sail laser and Shake a Leg might be too low level.
So, I can see how you might have looked at all these but not found a match.
You might try http://www.arcmiami.com/school.htm
or CGSC Adult Sailing Programs
or Sailing Home
Aquatic Rental Center, Coconut Grove, or Castle Harbor look like they might work for you.