Ok, here's an update.
We went on another 4-night trip. Having charged the battery for two weeks on the converter.
Night #1= Nothing-won't even power up the CPAP, even with inverter. BAD NIGHT!
Day #2= take out the battery on the passenger side of the TV (Dodge 2500 with 2 Batteries). Replaced it with Casita
Battery. Drove around for a couple hours. Scouted out new camp sites, checked on huckleberry fields, etc... Then swapped the batteries back.
Nights 2-4= ran steady on 12v supply, no need to get out the inverter.
Day #5= swap Batteries again to charge on way home. Swap back again, when home and put Casita
Battery on float charger.
It would appear my converter is not charging my battery. I've looked it up, it is supposed to charge my battery. Yet another thing the PO lied about.
At least I can now make sense of why my big Marine Battery provided less capacity than a tiny starting Battery.
I don't know that I'll replace the cconverter? I don't store the battery in the trailer. I may just get a quality 3-stage or two to keep in the garage.
I've also decided to go with two Battery systems.
2x 6v DEEP CYCLE on the tongue. To be used exclusively for my CPAP. Also to be powered by TV, while in transit.
Current group 27 (to be replaced by true deep cycle 12v when necessary) in factory location. This will be for lights
and fans. That way I don't have stress about the family stealing my "so I don't die in my sleep" power. It would be nice to run the MaxxFan at night, too.