Update:
Putting the limited slip diff. additive in the rear end fixed the problem. Pushing the car out of the basement is smooth as can be. No pop or binding feel at all. The fluid in the differential must have degraded over time. I don't know how old the fluid was. I drained the fluid about three years ago but did not put the additive in at that time, so the problem was still there. The driveshaft problem is not that noticeable so I'm leaving that alone for now.
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