If I could take a swing at your questions.....
I've had my Full FatSix in the deep sugar sand of the NJ Pine Barrens many, many times. The FFS comes with 80mm width rims and 4.0 tires. For truly deep sand riding, you need the width of those rims to support a wide tire, deflated anywhere to 5 to 10 psi for the best possible traction and float upon the sand. Go to any fatbike forum and folks there will say the 80/4.0 combination is at best, the bare minimum required to ride on sand or snow. Some of those folks are running 26 x 5 inch wide tires.
Not sure what kind of bike you are riding, but if you were to go beyond a 2.3 inch width tire tread, you run the risk of the tire rubbing against the chain stays, etc, especially when you go to air down your tires when going through deep sand.
PS: When running a fat bike, a good tire pressure gauge is your friend and a must-have, and
Nakto customer service can help with tips on maintaining optimal tire performance!