Continuity on hot/neutral at dead outlet
Thanks to @manassehkatz I went to all light switches on the same circuit and disconnected them. The outlet retained continuity.

I then traced the wire through the crawlspace to a wall with another light switch that I did not realize was on the same circuit. Opening that box and removing the switches I found that the line to the outlet comes from that box, and I somehow failed to reconnect power to the outlet when I was changing out my dimmer switches. The neutral was connected, but the hot line to the outlet was just loose in the back of the box. (Yikes.)

I'm not sure what connection it was making when everything was crammed into the box. I'm guessing it was loosely connecting to one of the free ground wires. Once I removed the switches from the box continuity disappeared. And, once I connected the wires properly, the outlet works again.