I wanted to do something similar, but running the CPAP off of the battery full-time so power outages wouldn't wake me, as well as be able to use it for light camping. The only major change this required was to seriously increase the size of the battery tender (4A unit), so it could keep the battery near full even with a full load applied (high pressure, humidity, and heated hose).
First, a couple pictures. The unit showing the 15A-fused cigarette output (the Resmed DC converter is rated for a max of 13A) and the SAE connection for the battery tender:

Inside (note the second cigarette socket fused at 5A in case I need to charge something while off the grid):

The battery itself is also fused at 15A using the fused connection that came with the tender. Safety first!
I've been running off of it nightly with no issues, and the tender keeps it fully charged even with the load applied. Links in next comment.