Interesting that orthodontics didnt fix your problem. It looks like your very prognathic, which is alright in terms of looks, but can be a problem when it comes to keeping your mouth comfortably shut at rest.
A bimaxillary setback will likely do the trick. See some top surgeons and make sure they consider aesthetics, and not to push your jaws too far back relative to your skull. a straight profile (straight line from the nasion to the mandibular incisors, with the maxilla slightly in front of this line) should be the most it is set back. nothing worse than being retrognathic.
Airway size should also be considered. I imagine since people with OSA who have their jaws moved forward often have their symptoms relieved, have the jaw moved back could cause a problem. make sure to have a measurement of your airway and how much the setback will reduce it.
