@brdross don't laugh but -- you could try taping your mouth while jogging. Mouth taping is a thing, which I've been using during sleep for 18+ months. It helps prevent dry mouth in the a.m. which I loathe. Can't sleep without it! Athletes are known to use mouth taping to improve performance and regular people too.

Check out these two books: Breath: The New Science of a Lost Art (Nestor) and Close Your Mouth: Buteyko Clinic Handbook for Perfect Health (McKeown).