Assateague Island on the Maryland coast has very soft sand. We have lots and lots of TC's and other 4X4's of every description that travel over the sand, fish, surf, camp the whole deal. We are required to carry a shovel, 18X18X3/4" wood pad, a jack, and a sturdy tow line. We air down to 20 psi front and 30psi rear, with a very heavy rig, and some time let more out if conditions warrant. Most of the larger TC's use 4X4 lowrange, drive slow (Speed limit is 15 mph), and still occasionally get stuck when extra soft or very wet spots are encountered.
On Assateague there is almost always someone who will help get you unstuck. Just letting a bit more air out, backing up a little, will free up the rig. Slow easy take-offs are needed. If somone spins wheels and buries to the frame, jacking up each wheel, and filling in with sand, usually will work. There are a large bank of air stations at the beach entrance to refill the tires.
With a permit, overnight camping is allowed for as long as the tanks allow, in a designated place, the Bullpen. If your able to get here it is a most unique National Park experience.
Google, Assateague Island National Seashore for all the info. We have found that, mostly, every beach area has its own problems and solutions. That there is no substitute for local knowledge. We are on Assateague in the You Tube piece below.