But my question is, what other parks have airstrips (especially around the Southeast) that would be worth checking out?
Well... 3D2 is right across the road from Peninsula State Park in Door County, WI (the thumb part of the hand). The airport and the park are both really nice, but not something you'd want to go out of your way for. Good for if you're passing through on a flight-camping trip.
Jackson Hole airport KJAC is inside Grand Teton National Park, but that's a big park and there really isn't anything walkable from the airport. In fact, if you didn't know better, you wouldn't realize it's in the park. It is the only commercial airport that's inside a national park.
One of the best in terms of being scenic, remote, and quiet that I've been to was 1Q5 Gravelly Valley, CA which is in the Mendocino National Forest. I had to buzz the runway to chase a pair of elk off of it to land. There are campgrounds within walking distance of the strip according to Google Maps:
Johnson Creek Airport near Yellow Pine, ID 3U2 is its own destination. The facilities available right on the field pretty much make it its own park, even though it's owned by the Idaho Division of Aeronautics. Camping here should be on every camping pilot's bucket list. Be sure to visit the spring-fed hot tub on the side of the mountain.
Not a park, but Ocracoke, Hatteras, and First Flight airports on the Outer Banks are owned by the National Park Service.
As is Jackson Hole. Quite a few backcountry airports are owned by the NPS or USFS as well.