Re: What to do?
Actually all scenarios use screws to compress the glue to a thin film. Since you are directly addressing vibration and resonance, the screw density does not create a problem with conduction.
The glue goes in between sheets of standard drywall, noy on the stud edges. Damping requires surface area. There is insufficient surface area on the edge of a stud to provide damping.
The Soundproofing Company