As what you are describing is running a P/Cpap overnight, and the power consumption of most of these (that I have located) is too high to run from any convenient battery bank more than over night. If your uncle is Daddy Warbucks, maybe you can afford enough lithium to do two days, but you are still stuck having to fire the APU regularly.
My suggestions based on what I learned helping a good friend with this very same issue but about a year gone....
- Change the house back to a pair of GC2s (probably should do anyway)
- Search up a device with lower power requirements and can run from the 12V system
- Swap in a good converter/charger. It should be at least 3 stage. Progressive Dynamics and Iota are two names I know.
- Install a REAL battery monitor that reports everything that matters. These will probably be either Bogart Trimetric or Victron Energy. The sub 50$ things on EBay have so far been unreliable.
You can't count on enough sun and solar to do this, so just make a plan to run the APU a couple or three hours every day that you are not on shore power. No matter what the state of the house bank, getting it from 90% to full will take a couple of hours. (This can't be rushes - Chemistry.) But if you plan things right, you can be a 90% by bed time and 60~70% in the morning and then you have all day to recover the bank.
Matt