I spend quite a bit of time playing in the California Desert. In fact I'll be heading out there for the weekend in a few hours. I'll vote for Dirtgripz or a similar tire. 11.5 to 12.5 wide. Use as tall a tire as you can reasonably fit without interference. Something with extra thick (E rated) sidewalls to deal with the jagged rocks. Air them down to like 13-15 lbs. for good stable contact, shock absorbtion, and floatation. For good bite, they should be luggy critters with a decent amount of void between the lugs. The sidewalls should be fairly tall.
If you go with a thinner C or D sidewalled tires, to obtain the desired squish factor, air up to a higher pressure. Obtaining the right amount of air-down is important to keep you from sliding on hard surfaced rock laden corners. They do need to be stiff enough to minimize body roll though. Use some strong cast smaller diameter rims. Not steel. Use some fairly stiff shocks in the rear, or/and split your rear bumpstops since riding on the bumpstops kills your traction at any appreciable speed.
At the risk of sounding conceited or arrogant... Actually,, to haul @ss across the Ca desert. I'd pretty much set it up like mine.