I would inspect the U Joints in the drive shaft. Easy to disconnect the front and drive the Jeep and diagnose. That’s where I would start, if that didn’t show to be the cause, I’d pull the rear then run 4H and see.
Doesn’t hurt to balance and rotate tires but your description doesn’t make me think that would be the issue.
I’d go front then rear shafts, but doesn’t hurt to inspect the front axle U Joints as well.