Installing 750W Inverter

My wife uses a CPAP machine that she needs to sleep. It draws quite a bit of power so I needed a fairly high power Inverter. High power inverters need to have either short wire runs or really big wires. In the past I have tapped right off the 12 volt terminal on the converter and ran an extension cord to the CPAP Machine but this year I wanted to install a plug next to the bed so that I would not have a long cord going from one end of the trailer to the other. There was already a plug where I wanted it so my Idea was to install a switch that would let me change from shore power to the inverter  when we had to shut down the generator and she could use the same plug regardless of the power situation. This drawing is what I came up with. all of this wiring is under the dinette bench with the electrical panel and I have mounted the inverter there as well. I will post pictures of the install when it is done. The only Thing that is missing from the schematic is there is a 60amp inline fuse in the 12volt line for the Inverter.  Excuse the missspelling of schematic in the drawing just noticed it. 

I didn't re-read much of this thread, but here's a 4-page discussion you can look at.

Have you tested it with something like a Kill-A-Watt so you know what amps it draws over time?  I imagine the heater cycles on and off so you'll need the average per hour.  

Does your wife have a newer machine, if so they run on 12 volt check your manual. You can get a patch cord made at battery plus or shack. You will not be able to use the heater but you should not need it in the summer.

Seanl, those numbers don't add up.  Dividing that up would mean 5.75 amp-hr at 120 volts, or over 60 amps-hr from a 12 amp battery.  That would kill a battery in less than an hour.  From what I've read people can run these for 1-3 nights from one battery.  That's why I asked if you did an actual measurement on it, that's the only way to know for sure.