It finally occurred to me that I had set my "Peer listening port" to something other than the default port (51413). I did that in accord with the instructions in Transmission Help, which read:
I had selected a port in the 54000 range, which was something easy for me to remember.Open Transmission, go to preferences, and enter a number for the port. It is recommended you pick a random number between 49152 and 65535. Let's use 50001 for now. Then quit Transmission.
Anyway, since I didn't know what else to try, I decided to try resetting the "Peer listening port" to the default selection of 51413. The port was successfully auto-mapped and I was connected to the seed and 4 leeches (5 of the available 6 peers) in no time flat. Several more peers also appeared in a second small-swarm torrent that I had running.
I don't know whether this was a fluke -- I might just have picked a lousy port -- or whatever else, but if anyone has picked a "custom" peer listening port and is having a problem connecting to peers, I suggest that you try the default port instead. If it's not a fluke and there are many other ports that produce the same result, I suggest that the Transmission Help "Port Forwarding a Router" page be revised to suggest that the user try using the default peer listening port before testing a custom setting.