I called Chris Coffee, and their excellent and friendly technician described a similar problem that he saw recently, where a leaking pump had damaged the motor. He replaced both.
I pulled the pump off, and lo and behold, I found a whole bunch of wet crud in the cavity between the motor and the pump drive shaft:

I then removed and disassembled the motor, and found that the ball bearing on that end was "grinding". It also looked terrible:

Interestingly, the corroded bearing was a KBF part that didn't look very well sealed against moisture entry. The bearing on the other end of the shaft was an SKF part, and looked to be of a higher quality (although I don't really know anything about ball bearings).
So I went to a local motor repair shop and picked up a replacement bearing (equivalent to SKF #6202-2Z) for $5. With a bit of judicious tapping, I replaced the bearing, reassembled everything (hate putting those side covers back on!), and my 1 1/2 year old S1 is nice and quiet again!
Of course, I will change out the pump as soon as a replacement arrives. Hopefully the crud won't build up too quickly... there is a small drain hole in the shaft cavity, but it was plugged up by the crud. I wonder how often these pumps leak. It would be great to be able to replace just the shaft seal, but it would probably be hard to get just those parts.
Question: do I need a PF manometer in order to set the pressure on the new pump?