So I fixed our washing machine. I am now expert at diagnosing problems with direct drive top loader washing machines, if anyone has a problem. The problem with ours was that it would not get up to full speed during the spin cycle, leaving our clothes soaking wet. The problem was that the clutch (a piece which mechanically fixes the motor to the inner tub during spin) was old and the pads were worn down, as can be seen by examining all of the black melted plastic debris here in Fig. 1.
Replacing it with a new one involved detaching the washer from the cabinet, laying on its side, unscrewing the drive motor and gearcase, replacing the clutch, and re-assembling. (Fig. 2).
Now the washer works like never before, it goes so fast during spin, its scary.