Last year we spent a week at Fiesta Key (just south of lower Matecumbe key (around mm71)), they have both campsites and cabins, and you can leave your boat for the week in the water tied to mooring balls (they also have full boat docks for power boaters). I understand they are under new ownership, so check them out first before committing to anything.
Here is our TI on the mooring ball for the week
You can cross to the Atlantic side under the nearby bridge if needed. There appear to be lots of flats and trenches in the area.
We don't fish at all, but we do dive and spear fish, so we are all after the same stuff.
If your down there make sure to stop at Robbies and get the Lobster Bisque. (you can probably launch from there also).
That area is very large, we had no problems covering 15-20 miles with our TI (with the motor and massive sails), and the TI is more equipped for open rough water, so be careful out there with a PA.