I'll chime in and say that's definitely too narrow a wheel for a 31x10.50, and it's going to cause a LOT of rubbing on the lower control arms when you turn. A 15x7 would be OK, and they're everywhere. A 15x8" would be even better, and they're pretty common too. (Gambler, Ravine, Canyon...) Keep the 15x6's for a trailer, and run 30x9.50's or 235's.
As for airing down, my experience, which is significant, has been that a narrow wheel PREVENTS you from losing the bead, as the tire is pushing harder against the bead, vs stretching a narrow tire over a wide wheel. Don't get me wrong, if you're running single digits in the rocks, locked, and getting rough with it or leaning hard on a tire, you can pull a tire off the bead even on a narrow wheel. But, if you're driving your vehicle like it has to get you home, you're probably no lower than 12 or 15psi, it's pretty hard to pull a tire off the bead at those pressures. (I wheel a lot at those pressures, in the rocks, and locked, and I have yet to lose a bead. In the sand, I run 5psi or so, and even with some moderate horsing around, I haven't pulled one. IMO, Beadlocks are WAY over-rated for general offroading.
<edit>
Oooh, Gaucho919's pics do look cool. I suppose I should temper my response to suggest that they might now wear real well that way, but they will fit. The rubbing on control arms is still a concern, but some 1" wheel spacers would help greatly!
C