Follow-up to this question:
I opened up this same washer to diagnose the problem, and found the drive belt in shreds with major gashes and barely holding on, and the whole interior (outside the washing basin) covered with lines of black grease matching the height of the drive belt, and with yellow oil all over the inside floor. There was cottony white (possibly plastic) fluff in several places as well. It looks like the drive belt was actually hitting one of the support struts, almost as if it had gotten stretched and the tension wheel had pushed it out too far.
I have replaced the drive belt and heard no major noises except those as discussed in the original question (thumping after washer stops driving a spin cycle but while the basin is still spinning).
I talked with an appliance mechanic and he suggested a test to see if the problem was the transmission of the washer: run an agitation cycle and see if the basin spins with the center shaft. The result was that the center shaft turns one way, then turns the other way, and the basin turns opposite to the center shaft on every other center shaft turn.
Is this test and result sufficient to decide that the problem is not the transmission?
I'm sure the oil/grease is indicative of some problem; any suggestions on what this might be?