Doh! Yes, that's right. 12.8 V is what I should have said. That's a freshly charged, new automotive battery. 13.8 V is the average voltage between 12.8 V and 14.8 V. I guess that's why most car audio equipment is specified at 13.8 V.
And you are correct that it quickly draws down from there. My car is about 12.3 V with the dome light on and not running. When the car is running, the charginng peaks go to 14.4 V and the average voltage while being charged is around 14.25 V.
It looks to me like the thing to do is just use an adapter cable without a regulator and just resign myself to charging the Walmart battery while the car's not running. (That means no charging during the road trip, I guess.) Either that, or get a dedicated 12 V battery to use as a recharging source at the festival and make sure it's charged up ahead of time.