Blackpool..
We recently went camping, and what I used for the bipap was a much smaller expenditure than what you are proposing, and weighed less too.
I went to Walmart and bought a Quipp brand "Power Pro" Autopower 300A. Once this is charged up it will run a bipap for several hours. However, you will still need a power inverter. The first power inverter I bought was not powerful enough, and the homecare that handles my bipap was of little help (the tech said he didn't know, just to go to Radio Shack) so, I took the bipap along with the battery booster into the local radio shack, (to make sure I purchased the right one). It is simple to use this, and the entire cost was way less than $200.
Size and weight wise, it would easily fit into a small carry on, along with your bipap machine. It would be heavy, but really, if your bag had the right dimensions, it would even fit under the seat in front of you for take off and landing.
The humidifier part of the bipap should not be used when its on battery power. Just plug your bipap into the inverter, and the inverter into the battery booster. I just happened to choose the Quipp brand, others here may know if other manufacturers make better ones. (but it was absolutely fine) I guess if you went to a Pep Boys or other automotive supply, you would have a wider range of 12V battery boosters. I'm not that familiar with the stores you have in Alberta. When we first plugged it in to charge it, it indicated it was charged fully right away (when it wasn't) It took several hours to charge it up all the way.
Unfortunately I can't help you with the air travel guidelines, which is ironic as I worked for so many years as a flight attendant... the airline representative you've been working with sounds like she is easy to communicate with though.
You would be much more comfortable wearing the bipap, or at least having it within easy reach while you're flying. The air is pretty thin during the cruise portion of flight.
Good luck and have a great time!