I was hoping you'd build a real mini buggy with a bike or sled engine, but if you've got a pile of Hitler's best compressor pumps laying around... *
If it's just going to be a play car and you want to utilize another of your boxers, how about a full tube version of a VW Thing with the same suspension as you outlined above? Sort of like a big SXS.
It would be nice and easy to get in and out of, would draw crowds where ever it went and would be a rare sight around the desert and dunes.