Can neurotransmitter imbalances be a primary cause of sleep apnea, such that double bi-maxillary advancement will not cure? If so what tests should you have and what type of doctor should I see?

Sleep apnea. Sleep apnea can be either obstructive or central. Correct diagnosis by a witnessed, overnight sleep study at an accredited center is essential. If obstructive, see an ENT to rule out obstructions ( deviated septum, tonsils, adenoids). If the lower jaw is retruded , causing blockage of the airway, a neuromuscularly determined appliance made by a dentist can avoid the surgery.
Sleep apnea and NT. Sleep apnea can be central (from brain) or obstructive (from oropharynx and blockage of airflow). Only the latter cause is treated by the surgery or procedures to change the anatomy of mouth and throat. A sleep study (polysomnography) and clinical exam of oral structures will sort out. The central causes are related to but not always caused by neurotransmitter issues.
Sleep specialist. Central sleep apnea and other sleep-related breathing disorders should be investigated for. Consultation with a sub-specialty trained specialist in sleep medicine (e.g. Neurologist, pulmonologist, etc.) is recommended. Good luck. (was an oral device such as a mouth guard tried before the double bi-maxillary advancement?).