OK, so I got a call from Tesla about what was causing the problem. Unfortunately it wasn't much help to me but maybe it means something to someone helping me out on this thread. They said the fault was coming back as a charging cable failure, and they offered to get me a new Tesla cable thinking that I was using theirs. I explained I was using my own charging station and not their cable and asked for more specific info but they didn't have any.
I'm guessing (?) that it is a problem with the Voltec charger. My Volt used to hiccup on a charge once in a while as well so I suspect it is not working properly. Unless someone has some troubleshooting ideas, I guess I am going to go the NEMA 14-50 route. Seems like the cheapest, easiest way to go.