Once again, thanks to all.
A'Oop, I was referring to this JAMA article from last year: http://www.salterlabs.com/store/downloads/107.pdf Together with what you sent me via FunGuy (Ah! Just got the joke on that one), it ought to convince anyone--even a neurologist!
(And, after the 02 guy asked if I had a license to buy the O2, I didn't have much choice but to try to prevail on his potential sympathy for a CH sufferer. He actually told me that they were not allowed, by law, to sell 12-15 lpm O2 (in Virginia, outside DC). But maybe he was just sick of me by then. Suggestions for an improved strategy are always welcome, though I guess for now we'll wait on the forthcoming appointment -- and move on tomorrow to phase 2 of RC busting.)
I've been sitting up with my kid as she endures this middle-of-the-night horror, and I think of all of you as she goes through it and then somehow manages to face the next day with hope and a smile.