When I get some time I may be able to resurrect my old scouting maps of the island for you. I've shot two does there in the years following the flood of 2010, and I have not used a 4-wheeler for either one.
A deer cart is very handy and practical due to the flat terrain. Thermocell is a must!! Especially for afternoon hunts, but they can be bad in the mornings too unless it's quite cool.
The campsite will be safe, but not as quiet as camping in the woods, since it's reasonably close to a bumpy road that big trucks run down sometimes. They just give you a flat spot of dirt - there's no hookups of any kind. The TWRA guys have a little camper trailer set up for the officers.
When scouting, look for persimmons and locust (bean pod) trees in close proximity to tree funnels formed by fields, creeks/ditches, and/or heavy thickets. My highest deer sightings were in pockets of trees with food beside large thickets...I think that's deer hunting 101 anyway. There are a few oaks on the island, but they are fairly rare. Most of them are concentrated in one area, and it gets a higher than normal amount of hunting pressure, so I usually don't bother with it.
You have reasonable access to about 20% of the island with the roads you can drive your truck on and hike from - bike/ATV is needed to get to the rest in a reasonable amount of time (hunt able area is something like 6,000 acres). If it rains, they will shorten the amount of road you can drive on.
Hunters tend to "claim" spots on Thursday by hanging stands. This can work in your favor a bit, because you want to find a place with no stands :).
If you run into trouble and need help, I work about 8-10 minutes from PI - give me a shout if you are in a bind.