Today, I came downstairs, pulled the transport, replaced the offending belt, and put everything back together. Then I put a brand-new DAT tape in and let it run for a bit, because I didn't trust it to behave and I didn't want to start with something irreplaceable that I really needed.
The brand-new DAT tape worked fine, so I moved up the irreplaceable scale to my recording of the Black Book Band concert at Duckon a few years ago. When that one passed muster, I put in the first of my old master tapes: Julia Ecklar's "Walkabout".
So far, so good. I have a little bit of work to do on the first track and some clean up to do, since this is a nearly 20 year old master tape intended for cassette, but it's looking good at this point.
Keep your fingers crossed for me.