For what it's worth I work at the Imperial Sand Dunes in California (and the Glamis dunes to the north). I've done everything from drive straight thru the middle of the dunes (honestly not the best idea if you don't need too- fun if it's your weekend trip, but risking getting stuck on a daily basis isn't fun) to the easier vehicle paths that people use for most of the year to get to certain bowls and valleys.
My work truck's tires are non-beadlock. I'll run 20psi if I think I'll only stick to the common vehicle paths, just to ensure that if I slow down for anything I'll be ok. If I get stuck I'll drop it to 15psi. This has gotten me out of trouble most times, but in some conditions (summer dry sand, low point in a bowl or dip, etc) I needed another truck for help. The lowest I've ever been is about 12 psi.
All I can say is that I've never popped a bead but I'm wary of doing so at 15 psi and below. I carry onboard air and pump it back up to 17psi or so after I get unstuck.
If you're jumping and carving on the slopes then I wouldn't go under 15psi for sure without beadlocks- in fact I'd keep it at 17-20psi until you need it.