It's good that your problem was solved, but your reasoning was faulty.
CPAP is not useless when obstruction occurs during exhalation. It does not simply act during inhalation to add airflow: the purpose of CPAP is to maintain pressure (i.e. inflation) throughout the breathing cycle.
As an analogy, consider blowing a lungful of air into a balloon, and then letting it deflate completely. That's normal respiration, and depending on the balloon material, it may collapse when it's completely deflated.
Now take the same floppy balloon and blow a small amount of air into it, enough to make it slightly taut. Then blow another lungful into it on top of that, and then let only one lungful out. There's still some residual air in the balloon, which isn't allowed out. That residual air ("continuous positive pressure") keeps the balloon slightly taut until the next lungful goes in. With each cycle, the same volume goes into the balloon and out of it, but the balloon is never emptied and so it never collapses. That's basically how CPAP works: instead of operating from 0 cc to 500 cc, your lungs operate from say 200 cc to 700 cc*. The point of CPAP is to prevent lungs from fully deflating without reducing actual air delivery.
- of course, your lungs are never really empty. Also, I made up the 200 cc figure, in reality the machine monitors pressure, not volume.