You're gonna need to wake up wayyyy earlier than 9 to get your run in - it's hot as heck! Ha ha!
When I was there (Feb, 2005) I had to do a 14 mile training run (for a marathon) - I started at 7am nearly melted! Fortunately we had a pool (Exotic Caye) that felt SO good!!! I ran from EC south to the park (?), then back to the ferry, then back again until I got in the mileage (I have a GPS unit).
Watch out for the taxis!
(Oh, and I'm from South GA, so I know heat & humidity like you do - but I still melted
)