Rear axle not centered

That is one problem to be addressed and it might solve the one being discussed here.
What is the correct procedure for getting things tightened? Leave everything loose and tighten on the ground? Anything I can tighten while it’s in the air?
 
What is the correct procedure for getting things tightened? Leave everything loose and tighten on the ground? Anything I can tighten while it’s in the air?

Right now every bushing that was tightened with the axles hanging are loaded with the weight of the Jeep when it is sitting on the ground. This creates excess wear and tear on the rubber and it is adding some amount of ride height. This added ride height will shift the axles to one side.

With the Jeep on the ground, loosen every bolt with a rubber bushing. There will be a pop as each one returns to a relaxed position. Little by little, the ride height will decrease and the axles will shift back towards where they ought to be.

Once the bind has been released from the bushings, tighten those bolts again and reassess what is going on with the axles when the Jeep is on the ground at it's natural ride height.
 
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Right now every bushing that was tightened with the axles hanging are loaded with the weight of the Jeep when it is sitting on the ground. This creates excess wear and tear on the rubber and it is adding some amount of ride height. This added ride height will shift the axles to one side.

With the Jeep on the ground, loosen every bolt with a rubber bushing. There will be a pop as each one returns to a relaxed position. Little by little, the ride height will decrease and the axles will shift back towards where they ought to be.

Once the bind has been released from the bushings, tighten those bolts again and reassess what is going on with the axles when the Jeep is on the ground at it's natural ride height.
I'll grab some cardboard, a few Advil, and give that a shot. If that doesn't fit it, I'll remove the track bar and see if it's bent somehow.
 
It would be interesting to compare the ride heights before and after you fix the bind. Measure the height of the coils before you start. Measure again from the same points when you are done.
 
If its stock height and your having trouble getting under there to loosen/re-tighten said bolts, you can rest both axles on jack stands so you have more room.

X2 to the bounce of the rear end. I would do it twice, once while everything is loose, and again after torquing.
 
The bouncy thing, if that really can somehow reliably center the axle to begin with, is only relevant to an adjustable track bar. With the stock stuff, there is only one place the track bar can go regardless of where the Jeep settles after bouncing.
 
So I took everyone’s advice and loosened the suspension in the rear. Dropped it to the ground, gave it a very good bounce / shake to loosen things up, supported the rear by the axel, tightened everything back up, and... no difference. Axel is still off center. I tried giving it a bit of a push while it was in the air and loose but couldn’t get it to move more toward center. Really at a loss here. My thought at the moment is to try driving it around the block to see if it’ll center itself (doesn’t rub when on ground but only by 1/4”) or have it towed to a 4x4 shop to have them try (closest one I know of is 1 hour outside Boston though).
 
With the Jeep sitting on flat ground, measure how tall the springs are.
 
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