You CAN do a re-circ system in the desert but it's not as easy as you'd think. It took me over a year to gt all the kinks worked out of my system. I'm having a hard time picturing what you describe in my head so I'm not going to make comment on it. The main problem with doing wet processing in the desert is that you have to haul in your own water 99.9% of the time. DO NOT use water out of a water trough for cattle!!! It's against the law and if you get caught..... Nuff said.
I've run "Long Toms", "High Bankers" and "Drop Riffle" boxes as re-circ setups out here and all have worked pretty well depending on the make up of the materials I'm running. The main problem is logistics for the water. When I'm going out for a 2 week stretch, I bring 165 gallons in eleven 15 gallon barrels. (Easier for my old back to handle the 15s than 55 gallon barrels) That's roughly 1320 Lbs of weight in water alone. Add to that the rest of the system, food, tent, drinking water (I'm NOT drinking out of those barrels!) and all my buckets and digging tools and I'm pretty much maxed out on weight.
If the area you're going to be heading out to has a lot of black sands, you may want to consider a drop riffle box instead of something with riffles and carpet/moss. I found that in many areas you might get a half bucket run before the carpet/moss is packed up with black sand. After that you're flat boarding and loosing gold. A drop riffle box will catch the gold but allow a lot of the excess black sand to rinse out.