Elevate your head a bit more.
Sleep on your back.
Try practicing breathing deeply or through your nose.
Brush your teeth directly before bed (?).
For decreased moonlit salivation, avoid nighttime sour or sugary foods, but perhaps have a salty snack.
Also, if you are drooling for more, visit here and here.
Check with your doctor to make sure you do not have a condition, like Diphtheria or an allergy.
Sleeping with your mouth open will not dry out your mouth. It will give you a sore throat, but clenching your teeth can give you serious health problems, though closing your mouth might help.
As a last resort, duct tape your mouth closed, your arms together, and close the trunk behind you. Good luck with your moist dreams!