Using advice on Appliance Parts Pros, I ordered a new drive hub kit. The wash plate (agitator) was difficult to remove. Used advice off of online videos to slide a thin strap under it, and wiggle and pull. Also used penetrating oil sprayed into splined shaft area. I was then able to access the drive hub and found the splines completely stripped out on this nylon hub.
The hub I had ordered would have fixed the problem, but the splines on the gearcase output shaft were also damaged from the nylon hub slipping on it for so long. I ended up ordering a new gear case, and installed it along with a drive clutch kit, drive belt, and the previously mentioned drive hub kit. I basically ended up replacing most of the drivetrain. This was not super easy to do but is possible with some mechanical skills and watching repair videos on Appliance Parts Pros and other online video sites.
Washer operates like brand new now. Very pleased with all aspects of my interaction with A.P.P.