Eventually I figured out that the problem was that the steam vent was clogged with some mush (I assume 20+ years of paper label bits from re-used jam jars, etc.). The mush was inhibiting the return-flow of the water jets shooting into the vent, so the water came out the steam vent in the front door.
(I cleaned out the gunk before I took the photographs.)
I used a flat-head screwdriver to pop out the vent cover (ours has snaps on both sides).
The vent and the cover were super-gunked-up with some unknown mushy stuff. The photos are only after I had already cleaned most of it out.
After removing most of the mushy gunk, I snapped the vent cover back in.
No more leak! :-)
(If you are doing dishwasher maintenance, you might want to check for clogged jets in the spinner arms. I make a very small (maybe 1/8th inch) hook at the end of a paper clip with a needle-nose pliers to pull out clogs from the jet holes.)
