I use a CPAP machine too. You're right, they are noting short of life-changing.
I haven't had the need to run mine off the grid, but if I did, I would go with the 12 volt adapter. They are available for many CPAP machines.
With an inverter you chew up electrons converting from 12 to 120, and then again when the machine's power supply converts the 120 back to DC - often 12 volts. The difference in power consumption should be enough that a third battery is not necessary.
You may need to add a "cigarette lighter" outlet over the bed, but it would be easy since the reading lights are 12 volt. Much simpler than wiring in a third battery!
The 12 volt adapter for my Philips machine is only $29 online. Use the inverter to run the TV.