Many thanks for all the contributions so far.
I did get back to the dealer. The dealer put the meter on it and seems to think the converter is charging properly.
One of the cells in the GEL Coach Battery was VERY HOT. So they seem to think that one bad cell started the problem.
The other two liquid house batteries had also swollen out some. But then they resumed their old shape after cooling down. The dealer seems to think those 2 MIGHT be ok. But I expect they will need to be replaced as well.
Monday I will start by checking the charge level again, then replacing the Coach battery, then evaluating the other two.