I don't know much about the Everglades, but it seems to me that a map might not be of much use since it is flatland. No landmarks = map useless. The compass is therefore also basically useless. The compass can only do a better job than the sun if the sun is obscured by clouds and the person is totally lost. Even then, the sun always sets in the west. If I was going to move, it would only be during daylight hours, and only in a direction I was certain would bring me to a road relatively soon. I think GPS would be better than a map in the Everglades if I didn't know where on the map I was, but I have never used a GPS so I don't know. I assume they can pinpoint current location in relation to surroundings to show roads, etc.
Swimming with gators? Been there done that. If I was very inexperienced, like our hero apparently was, I would make a camp on some dry land and cook up some catfish and wait for rescue beside my signal fire.