I may be a couple months too late, but I think I the best option with no 12V outlets in the RV. I had a very similar issue. I am on a BiPap and camp a lot without hooks. I bought this...
http://www.walmart.com/ip/Schumacher-Electric-6-in-1-Jump-Starter/25955544
Cost about $100. I have used it for my BiPap for about 45 nights over the last 4 months and it has worked great. (use the 12V for better efficiency) I even use it to charge my cell phone during the day. I use the generator approximately 2 hours to charge it back to 100%. It will run at least 2 nights without being charged. I haven't tried more than that.