I don't believe that shocks affect the ride height; maybe a bit, but I can't see a bad shock(s) affecting it enough that you would see it. Usually the only way to make the back lower is longer spring bolts. I don't know enough about how to do wheel alignments to say if lowering the rear changes any of the alignment settings.
rear feels loose? Was obviously when the tire psi's were way off, right? What about after you adjusted the psi? No change? Little change? It was loose before the U-joint work, or just after the work, or both? I'd start looking at all the bushings, jez there's plenty of'em too. Maybe the batwing mounts? Sway-bar end links loose? Or anything that could be not T/Q'ed down to spec that came apart when the joint work was done. The C-beam is up to T/Q?
Sorry, I'm just tossing out stuff that I'd look at. I really don't have an answer.
Tom