If sleep apnea is due to autonomic dysfunction, what can be done to stop it ?

Depends on the cause: It is unusual to be caused by autonomic dysfunction. Usually there is an obsstructive problem.

Splinting: Obstructive apnea is often a "side-effect" of the body's self-preservation mode during sleep. The same mechanisms that prevent us from acting out our dreams (think sleep walking and its risks). When muscles are "paralyzed" in sleep, the loss of tone of the muscles of the throat result in partial (snoring) or complete (apnea) collapse when inhaling. CPAP or dental devices splint the airway open.

Improve ANS function: Your respiratory rate is controlled by your body's ph. If your ph is too high (alkaline), your respiratory rate will decrease as your body tries to retain co2 and become less alkaline. It is possible that excess parasympathetic tone can make you more alkaline and contribute to a deceased respiratory drive & predispose to apneic episodes. One would need to find & treat the cause of the pns problem.