Opened up the back, I can see a little trail of oil that has leaked down from the rear gasket (where the shaft goes through the external drum to spin the interior drum).
This is likely the source of the problem, according to what I've looked up on the interwebs.
Here’s a photo, you can see an oil residue trail down from the seal, and a tiny pool close to the bottom:
From the
Parts Manual, it looks like the part I need is this one - on page 7:
22 134509510 Shell, outer tub, rear, w/bearing, seal
It doesn't look like there's just a separate gasket or seal piece. The part is the whole back of the external tub. To get that off, I'm going to have to take a whole bunch of the washer apart.
Anyway, I'll have to see how much this part costs. Anyone have recommendations for a parts supplier in the city or online?