Some people report that singing -- singing! -- really helps their sleep apnea.
Dr. Stephen Park said that myology (which are exercises to strengthen muscles around the inside of one's mouth area) helps some. I think singing would be better. If you read all the FAQs on this (click below), I think you'll agree that it makes sense for some.
I've heard before that speech therapy, or singing lessons can help sleep apnea. The problem at that time was there was no way to determine which exercises help. Getting research done, rather than anecdotal would be important.