Gas (3.7L auto) and diesels are supposed to be the same diff; same ratio, trac-lok optional. There's a production change in 2005. Some diffs have the speed sensor in the pumpkin, others have one at each wheel.
The on/off the throttle part, have a close look at the rear upper control arm. The bushings can tear, especially with lift, and/or the balljoint can develop slop.
Assess the pinion for play. Even without play, the bearings can be worn and howl/humm. On our 2005, I didn't realize how significant it was until I renewed the bearings and there was noticeably less road noise. On a 2003 I swapped rear ends on, the pinion was so noisy it sounded like metal-on-metal brakes dragging/growl anytime the Jeep moved. Still no play in it though.
The slop - if it's r&p backlash - you have to pull axles, axle bearings, and seals to even get at the adjusters to take up slack, and re-check the pattern. At that point, might as well renew the carrier bearings.
Gear oil sounds normal if its been in there a while.
_________________ Hers: 2005 KJ, V6/6spd/NV242J/3.73/posi, 2" Teraflex, ¾" cradle drop, KK forks, 22½" hub-to-flare, RRO arms, 245/75R16s, 260,000km Mine: 1993 W250, Cummins/5spd/NP205/3.54, Lockright, ~3" lift, 315/75R16 Duratracs, extra smoke, more noise, 374,000km
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