Hi
OK .. I'm on CPAP too, since November 2009, and have fought with the identical problem.
All my life, I have been a flat-on-my-face stomach sleeper, varying only to get in the kind of positions you describe.
Check the gear:
This is the machine I am using
ResMed - S8 Escape? II
Here's the general mask page.
ResMed - Masks
Here are the ones they had to offer at the hospital.
ResMed - Hospital Full Face
I'd started with the full face mask and felt like a cross between WW1 gas attack and Bondage session.
So I went on to the nose only mask
ResMed - Hospital Nasal
Nose-only mask has been number 1 help when it comes to getting closer to my prefered position. Side-of-head against pillos is now no problem at all. Flat on stomach is something I don't do often now .. but with careful pillow positioning, I can hang my nose and nose mask over the edge of the pillow.
Number 2 is Latex Mattress ... it allows a far greater range of positions whilst providing precise support. I'm not referring to memory foam, or to matresses which have a layer of latex. I am referring to a big 10inch deep latex matress. Unlike memory foam, it gives instant response to your position choice or position change