Drying of the mouth may be a good thing since it warns you that you are not running the humidity high enough. In your case, stopping mouth breathing will only succeed in drying of the nasal areas. That make you more receptacle to colds and other infections.
Get that humidity up higher and the air won't be looking for moisture from your wind pipes.
I encourage you to just stick with CPAP therapy, it can take some time to get used to, but, over time, it does get better.
hang in there.
Like you I'm new to all this CPAP, sleeping, headaches etc world. After a week on a CPAP test machine I felt awful - ready for launching the machine out of the window! I took it back to the hospital (UK so NHS) and was issued a manual machine (they try and keep costs down), I explained that I felt worse, partly because having also COPD I tend to mouth breath ... with a nasal mask?
I tried a full face mask for the next 4 weeks and this just worked!! I had some issues with the silicone on the bridge of my nose and, like you, the really dry mouth and (bleeding) nose.
Revisited last Monday and they gave me a different full face mask that avoids the bridge of the nose and added a humidifier. The result being that I'm sleeping soundly and solidly for 6 hours a night (up since 4 this morning) but then awake for the whole day!
The humidifier has completely sorted the dryness and the mask seems better (not perfect as yet but I'll keep working on that because, according to this site, getting the right mask is key and can take some time to find the right one.
Keep the faith and try changing one thing at a time until it works for you - only then (like me) can you enjoy the sensation of actually being awake again!