The other side of the tree had sort of a partial driveway in place from where a bulldozer had scooped up dirt to help repair the road in the past.
I leveled out this area and also another one in back of the tree to create a suitable surface to drive on. Then I made an elevated platform to park on underneath the tree. I also created a levee to help protect the campsite in case of another flood. In total, it took a couple hundred five gallon buckets of dirt and rocks to complete all of the modifications (outside the tree and inside the tree).
The new parking area was much higher than the last spot. It was also much cooler, more private, and less dusty because it was under the tree and away from the road.