FWIW I had moderate sleep apnea (nowhere near as bad as what you're describing) and I "cured" it by forcing myself to breathe through my nose at least 90% of the time, including when sleeping. Some people tape their mouth shut, but I can't do that - I have a beard. Breathing through the nose seems to have fixed the permanently runny nose as well, I don't know why. I know it's all individual and what worked for me might not work for everyone, but IMO it's worth a try. The downside is, until the corresponding musculature regains strength you will feel like you're out of air. It'll take 3-4 weeks to fully adjust. It'll pass, don't worry.