Well, crap. Did the search on harmonic balancer as suggested by Gilly, and went poking.
Wife's wagon has a build date 04/01 and HB part number A112 035 08 00, both of which
should indicate a good part - but the rubber ring is clearly coming out.
Any comments re: DIY replacement of the HB? Some of the comments in
this 5 year old and running thread

make me think this might be worth paying someone to do (needing to buy "proper" $100+ tools kinda kills the savings if I'm only gonna use the tool once).
Crap, 'cuz it's one more thing to do/pay for, but great news since I found it before it died. Many, many thanks Gilly.