Wow! Panama City! I can see why you have surface oxidation in you Gel coat with the Sun you get down there.
I would be surprised if McGuire's 3-step finish restorer wouldn't work. It has an oxidizer remover (#1), then a surface polisher (#2) and then a Carnuba wax coat (#3). That usually works every time.
Of course, West Marine, your local boat supplier, has some stuff that works well on the Gel coat on my boat here in the Ocean State; West Marine Fiberglass Color Restorer (P/N: 492546) which takes off the oxidation and does a light polishing in one step, followed by West Marine's premium Polymer Polish (p/n: 4926450. Both should be applied with a power buffer, and don't do too large an area with that polymer polish or it'll dry like steel and you'll have to go over it again with the same polish to get it to loosen up and polish out.
good luck......gn