Problem solved!
I had checked continuity with the multimeter before and found no issue. I did it again: still no issue. Joe's suggestion about rail pins got me to look up close and personal at the switch. I didn't see any problem with rail pins, but there was debris between the ties, and nearby, I noticed a few very fine steel wires that had flown off a wire wheel. After vacuuming the vicinity, everything ran with no problem. It seems a small piece of fine, bare steel wire would intermittently make contact, especially when wheels were rolling by.
Thanks to everyone for your help. Such a relief to get this working again.