We have a good bit of experience with over sand travel. It's lots of fun. When we air down, 20 psi front and 30 psi rear, shift into low range 4X4, tune the radio to bluegrass, and cruise slowly south on Assateague Island, MD, our troubles dim and pass away. Make wide slow
turns, always stop on level ground, not facing up or down hill. If you do hit a soft spot, let out some more air and backup a little and pull off slowly, don't spin wheels and dig down to the frame. We have stock 16" rims with Nitto Dune Grapplers for sand and 19.5" "H" rated delivery truck wheels and tires for the highway.
We operate in very soft beach sand, using the above techniques, we travel freely. There are lots of other 4X4 vehicles and all assist each other when needed. The NPS requires a tow line, a shovel, a jack capable of higher lifting than the standard jack, and a 18"X 18" 3/4" plywood pad to sit the bottle jack on. I too have a strong air compressor, there are a bank of high pressure devices at the jump off point at Assateague Island National Seashore. Also you'll need a larger pressure gauge. The Bluegrass is optional but is a great attitude adjuster.