I'm not positive on what the conditions of the desert are but if it's deep sand the Mickey Thompson Baja belted tires did well here. I would not do a standard MT style tire (Like BFG MT) in the sand as it will dig in too much. You would want the widest tires possible too to keep you floating on top of the sand. For me the 31x11.5 Mickey T. Baja belted did very well in glacier silt and deep sand. No lift required just a little bit of trimming up front of the front wheel wells. The Baja Claws mounted backwards might do real well too.
But if a MT tire will work I can't believe how well my TrXus MT's do in all the conditions I have put them through. Not sure if they make ones that will fit, but most likely they do.
All the above tires give a descent ride.
2001 Ironman Daily Driver... 3.5" suspension lift (OME912 springs and 1" spring spacer), ball joint flip, 1.5" front diff. drop, 33"x12.5 TrXus MT, 16x10 Eagle Alloy rims, Interceptor, PV muffler, K&N air filter, Alpine Supercharger, Bilstein shocks, and some trimming.
2000 Ironman Project LS-1 VX... very slow progress but someday....... ohhhhh someday......