I now see what the other patient at Apria was getting at when they described sleeping with the CPAP as being "awash in black ink". I have been in sleep that deep before, but not often, and it always left me feeling dazed and confused. I gather, however, that this is what sleep is "supposed" to be like for most people.
Same again last night. After 5-10 minutes of fidgeting and trying to get the mask right so that it wasn't pinching, wasn't smooshing, and wasn't shoving whiskers up my nose, I drifted off, and... WHOMP!
So apparently, the thing works!