first, you mention it uses 12V 6.6A. if it has a 12V input, which is very very very common, you don't need an inverter, just a 12V adapter plug.
Second, it likely only draws about 2A on 12V or even less. My advice is that if it has a humidifier, turn that feature off it at all possible. that is the biggest power draw. Same with any wifi it may have or tube heater. Manual will tell you how to turn that off.
Then, you can run it off a 12V outlet in the trailer and you should be able to get multiple nights off even a single 12V battery.
I have a resmed cpap. with the humidifier turned off it uses about 6AH or less in a night. thats less about a 1A draw. I can run it 3 or 4 nights off a 250WH (20AH) lithium battery pack.
Don't know the AH of a group 27 but say it is near 100AH. drawing down to 50 percent is 50AH so you could go 3-4 nights. Now, more than likely other things you use will draw more each day.
Now if you use the humidifier, you will likely draw around 25-30AH, still ok for a single night.