I would say that if you checked the u-joints and exhaust, and they are good, then its something in the rear suspension.
Possibly a broken center pin, loose u-bolts, Or even a spring bolt that has rusted to the eyelet will cause a similar noise.
Jack it up from the frame (or set it on jack stands) so that the rear end is hanging, then see what you have play in.
'87 YJ, 4.2L built and bored, 8" of lift, 8.8 rear, AX15/NP 231J, Tom Woods drive shafts, Flat fenders, 12,000LB winch, Custom bumpers, Rattle can paint job. Never completed...