I ended up purchasing a 12v plug and a 222wh Suaoki lithium ion battery pack to power my CPAP for the trip. The battery came with a cigarette lighter 12v adapter, and it is really small for the capacity it provides. It's about half the size of a lead acid battery with the same capacity. I linked to Amazon because they have the most reviews, but I ended up actually purchasing one from Wally World's website because it was on sale for $130.
You can plug a 110 volt plug into the battery, but it's much more efficient to use the native 12 volts instead of converting it twice.
I used it last night with the humidifier removed, but I didn't change any other settings. I also do not have a heated tube. The battery pack has 5 lights to indicate the charge level, and when I woke up 4 of them were still lit. I couldn't be happier. I now have a solution to my camping problem, and a backup battery should the power go out.
Below is my DreamMapper page showing my usage last night:
