The display seemed to be reporting accurate voltages in your post #13 above. About what I would expect under the circumstances. Your engine alternator put a light surface charge on the bats in 20 mins of driving and the power you used quickly drained it off. What I don't understand is how you read the voltage at the batteries and get one number while the display shows something else. The most likely explanation is that you are making a better hot and ground connection with your meter than the display is seeing with its wiring.
I have to agree that the converter is not charging the house batteries, but the question is why. You can go ahead and replace the converter, but that's a $200 item and I would want to be darn sure before spending that much. PD makes good stuff, so a failure on a fairly new unit should be rare (but not impossible - I know of another that failed after only two years).
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL