Airing down will help a lot for the stalling. It allows the tire to conform to the rock and climb it less abruptly than when you're at full tire pressure. Think "oozing" over the rocks instead of bouncing over or off of them. Even going down to 18-20 psi helps a lot. If you have bead-lockers you can go down to 10psi and you'll hardly feel the bumps.
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