There is a secondary solution to CPAP machines that may apply to some people who find their breathing/sleep improves with sleeping position. About a year ago I got a Mandibular Advancement Device from a TMJ specialist that pushes the jaw forward, preventing the tongue from pushing the against the palate and obstructing airflow.

I had tried a CPAP machine previously and still felt that it wasn't working (although the data said otherwise, I just felt like I wasn't breathing properly).

If, while laying on your back, moving your jaw forward improves breathing significantly, this type of treatment might be a good alternative to a CPAP (costs are similar though).