On the day of my visit, I saw at least two or three of these rodents scurrying around the island. However, I am not so sure if this rodent is either a Marsh Rice Rat (Oryzomys palustris) or a Hispid Cotton Rat (Sigmodon hispidus)?
I'm inclined to say that this is a Cotton Rat as well. They're fairly common in Florida and the shape and coloration are right for this species (Sigmodon hispidus). They are very adaptable native mice and I see them at the Oklahoma City Zoo regularly.