Dry mouth means that the air must be flowing through your mouth either as a leak or as mouth breathing regardless of the humidity. If it is a borderline condition (of mouth leakage) then humidity may help.
I like the idea of the soft cervical collar but have not tried it yet. We had a member who stuffed on old sock and fastened it so the stuffed portion was under the chin. He said that worked well for him to avoid mouth breathing/leaking.
My experience with chin straps is that the ones that cup the chin keep my mouth shut but I still get mouth leakage because they do not seem to encourage me to maintain a tongue seal. Some people find that they work well enough. What worked for me is a 3 inch wide strap that goes under my jaw from chin to neck. My theory is that the pressure on the soft tissue under my jaw reminds me to maintain the tongue seal even in my sleep.
The other thing to consider with a chin strap is how to hold it on your head. A plain simple strap works for some but for me they slide off during the night. I need an auxiliary strap going around the back of my head.