You don't really want to use ordinary wood screws, but look for guitar or bass pickup mounting screws form guitar parts suppliers. Precision and Jazz bass pickups are both screwed directly into the body and normally have an unthreaded section by the head.
Though you can normally find larger sheets of that foam on eBay for a similar price. You'll just need to work out the depth of foam you need. Better to get something thicker than necessary as you can always cut it down, otherwise go a lot thinner and build it up using several layers.
Last edited by Simon Barden; 11-09-2018 at 07:55 PM.