A few years back, I spoke with AEV engineers at EJS in Moab. They were running the last gen. Grand Cherokee with the Super Lift 4.5 inch lift. We asked them how the vehicle performed off road and they told us it was so amazing that they never even engaged their lockers. The brake lock differentials made all the difference. My father has them in his '12 grand and my brothers have them in their '05 Commander and '12 Rubicon. (wish they were in my '05 Tundra) They have never slowed them down, just kept them moving forward. I used to have a Cherokee that was locked in the rear, and there are some hills (usually loose dirt) where I would lose traction and just spin. I can also tell you from experience as a trail guide for the Red Rock 4Wheelers EJS event, that you are not airing down enough if you are only running 20 psi. In my Cherokee, I would run 33X10.5
BFG ATs at 8 psi. I did not have bead locks and it was never a problem. I really out performed many others and they were always amazed. it took me years to be brave enough to run it that low. I started out at 20 and then 18 , then 15, 12, 10 and finally 8. I had one close call, but the tire always stayed on the bead. I believe from what you have said that you have figured out that when you have less air in your tires that your Jeep has better traction. BLDs will not make up for over inflated tires.