Do any doctors work with patients having disruptive sleep patterns not related to breathing obstructions? I am having a shortage of deep sleep, and non-standard sequencing between Deep and REM stages.

I'm confused! Based on your knowledge of your abnormal sleep pattern, it sounds like you may already have a doctor (sleep specialist) who works with patients with disruptive sleep. If your doctor feels your problem is "above his/her pay grade", s'he can refer you to someone with more experience and qualifications. Best wishes.