OK, I feel like an idiot, but that was the problem. I had the power wire plugged into the back of the meter in the "relay" slots. They look just like the slots on the shunt. Thank you Vic for saving me from replacing this!
Whew! That's great. FYI, while I was troubleshooting mine I found I had a bad data cable. The BMV always showed 14Amps charging, even when the SHUNT was disconnected from the battery! Surprisingly, this is a relatively common issue, as I found 2-3 hits on google searching specifically for "Victron BMV 14A" Strange!