IMHO, your symptoms sound worse than tires.
Yes, crappy tires can make you frown, but as bad as all that? Perhaps...
You mentioned the treads are not worn and the pressures are good.
You also mentioned that one wheel spins notably more than the other.
I'm clearly out-voted, but I liked your theory that one of the wheels is binding.
I have seen this happen once when a caliper was seizing, but it could just as well be the e-brake.
A seizing bearing would probably display other noisy symptoms.

Do you have limited slip? [Unsure if that was an option or not]
If not, I would suggest the following test:

1) Chock front tires, jack up rear end, set down [securely] on stands.
2) Release e-brake and put in neutral. Depress the brakes hard just once for good measure.
3) Double-check those jack stands.
4) Spin one wheel with your hands, and check for any binding or dragging. The other wheel should rotate in the opposite direction as you do this- if it does not, suspect and inspect the other wheel.

I have no experience with limited slip, but I expect the opposite wheel might rotate in the same direction when you do this test, though there may be some minimum speed 'threshold' before it starts to move. Either way, it should be easy enough to detect any binding that would be severe enough to cause traction problems.

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1986 300E 5-Speed 240k mi.