10 years ago, on the Burb we did have issues with the cooper made tires.
A Burb is a heavy truck.
BFG, has a great track record for us, balance very well. MTs or similar are the ones, noise just doesnt matter compared to no forward go in some mud. I have had ATs in mud, they turn to doughnuts, and iceskates. First hand at an event I saw the difference, the ATs had trouble, the MTs kept going (same trucktype).
The pictures look like may be try 2 psi, more next trip, and may be more yet. You could always air down to this on the picture if youre just in trouble. Certainly we have had our tires look that bulged on a obstacle before, when the whole truck is literally on one wheel. And amazing, touch wood, so far, so good.
Despite contactpatch, and ridesofteness, airing down help puncture resistance (to a point). An Aussie 4WD magazine had an article, about running over sharp stuff with different psi. And the aired down tire didnt get poaked, but folded over the object.