Waking up with a dry mouth is a classic sign of nighttime mouth breathing, and potentially hyperventilation. I used to always wake with a dry mouth, and often breathing heavy.

If you're able to breath through your nose, I would definitely recommend trying the mouth taping. I just use a very small strip right in the center of my lips (.5" x 1"), so I can actually still open the sides of my mouth and breath, which makes things feel less claustrophobic.