The first thing you need to do is look at your leak graphs and find out if you're leaking. If you are, your therapy is compromised, so that needs to be straightened out first. Being a mouth-breather is not the same as being a mouth-leaker. What happens when you mouth-leak is that your jaw muscles relax, your mouth opens, and the pressurized CPAP air escapes. Without trapped air the pressure splint can't be maintained, your airway collapses, and you suffer from obstructive sleep apnea just as if you had no CPAP machine at all.
If you are leaking, and a chin strap doesn't fix the problem, then you'll have to switch to a full face mask.
Once you get your leaks under control hopefully you'll get the rest you need and the teeth-grinding will stop. There's no guarantee, though, that that will happen.
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