Thank you all for the replies. I appreciate everyone's thoughts and assistance in diagnosing the problem.
Dan/Nickie, thanks for posting the towing procedure. I mostly followed that, with three exceptions that I would consider minor:
1. The engine didn't stay idling for a full minute at the beginning of the day. I've been lazy with this and should probably do more to keep the engine from shutting off early, like turning on the defrost and holding the accelerator down. I'll follow this more closely in the future.
2. I put it into Acc mode instead of Off, although it shuts itself off shortly after Iock the doors anyway (2013 manual says to put it into Acc mode).
3. I slightly exceeded the 70 mph limit once when trying to finish passing a truck and cresting a hill. I got up to 71, 72 tops.
Will/Angela, I especially appreciate your thoughts as a FFH owner. I can't say for sure that it was in neutral the entire time, but I'm sure it was in N when I discovered the problem and got in the car to press the brake pedal and make sure it started. I had traveled 300 miles that day but only 12 miles were logged. Maybe some bumpy stretches of the highway bounced it into gear and then bounced it back into neutral. The EV battery state of charge indicator showed 2 miles remaining both before and after towing that day.
I'm taking it to the dealer this week for regular service anyway, so I'll ask them to check everything out.