You didn't mention the height of your lift but I think ome lifts are 2 inches which would explain the very little vibes/no t-case drop situation...it's best if you have no vibes or you will eat through seals and u-joints but what "no vibes" means is up for discussion...everything that rotates vibrates to some extent and it can be tough to even poinpoint the source of the vibes, as you mentioned...switching tire front to back can help to rule out tire vibes. Have you considered full droop? if not you should raise the frame, let the axle (rear) hang and confirm that the wheeles can turn without the yoke ears colliding.
As far as alignment, I've given up on pro alignments and I've been aligning my jeeps myself for several years with no adverse tire wear. I just do it really carefully with tape measures and then use tape or paint to confirm even tread wear. If you are not familiar with this I could describe it further.
My neighbour may want those tires? age, wear, price, quantity?
I would try dropping the tcase a little, even if only temporarily and to confirm your suspicion of the source of the vibe. You may be able to install cam bolts on the rear upper control arms at the axle which would allow you to adjust pinion angle which could also help with your vibes.