Your tires sound like they have the inappropriately too-stiff Load Range D or E which means you have to air them down further than you would with the more appropriate Load Range C tire.
Even taking a more appropriate Load Range C tire down to 20 psi isn't helping at all, that's really not even airing them down at all. For any Jeep size tire, you have to get them lower than 15 psi before the tire can flex enough on uneven terrain to improve traction. I regularly took my previous 33's down to 10-12 psi and I took my 35's down to 7-8 psi without bead locks. You can take them down to 2-4 psi with bead locks.
JMT, I'd be taking your tires MT/R tires (essentially 31's) down to 10-12 psi without worry that they'll unseat. And Chris I don't know what size tires you're running but don't be afraid to go lower than 15 psi. You'll see a dramatic improvement in traction once you get below 15 psi.
It's harder to unseat a tire than most would guess. I've yet to have a tire unseat in 20 years of offroading.