After searching around for a tire that would fit my criteria I've finally found it.
The General Grabber AT2 in a 27X8.50R14LT

 The Maxxis tires that come stock new Rhino 700s are well suited for hunters, farm work and general activities such as trail rides, sand dune running and all-around use. However I recently found the limitations of said tires when riding rather aggressively near Lake Shasta, California.

The lack of available sidewall on the factory tires resulted in wheel damage when a simple driver error occurred. When this happened I felt cheated. Maybe it's just me, but I think a tire and wheel package on a 1,000-lb UTV should be able to survive such impacts similarly to the way a 37-inch BFG Project would on a 17-inch forged wheel on a Trophy Truck. So, I did a little research on what wheel and tire sizes the pros were running on race UTVs.

I was surprised to see a BFG A/T and General Grabber A/T in use at the races.

Another positive benefit to using these tires is that when I get around to registering our Project Rhino to be street legal in Arizona, the tires will be DOT legal as well.