In 2009 I repaired the back part of the roof on our SkipperLiner. Not wanting it to leak any more, and needing a temporary fix I bought a 12' x 10' sheet of black EPDM rubber. I asked the roofing supply guy what I could glue it down with. He had no idea, but suggested construction adhesive. So I bought a couple of tubes of this:
-- I ran a bead along the top edge of the rubber, and smushed it down evenly between the rubber's edge and the roof. Now, the roof was hardly 'prepped', as there's remnants of 3 different carpets and their glues. I didn't really care, this was just "temporary". It set up nicely, and I covered it up with some new carpet.
It worked so well I tried it to repair a broken fitting on the top of the 52 gallon water tank down in the basement.
6 years later, the glued edge looks exactly as it did on day 2, still completely glued down, no cracking or shrinking, and it's still slightly pliable, not hard- totally leak proof. And it's totally out in the weather, 24-7. The carpet isn't glued down, and many of the glue edges are always exposed. Same results with the water tank, even though silicone won't stick to these tanks, this stuff seems to! The repair has never leaked...
I haven't used it for holding screws, but I can't think of a better stuff to try! And since it does remain pliable, you'll be able to remove 'em too!