1" S-Type Screws OK for hanging 5/8" Drywall on short wall in basement?
yeah, you should be alright with the 1 inch drywall screws. The optional way to fasten any drywall is to have screw head slightly dimple the drywall paper (not penetrate or damage the paper) so as to have a depression for the joint compound. It wouldn't be a bad idea as you noted to use extra screws. I believe the fastening method is 6 inches along the edges and 8-10 inches in the field. As an alternative suggestion you could install 3/4 inch plywood strips behind the soundproofing strips. The extra 3/4 inches would allow a  1 5/8 inch screw.