How long were the screws? You've only got a thin pickup ring and the standard bridge pickup rings screws tend to be supplied longer than the neck ones.
You can cut down the screw so there's no point to it (except there is as it holds the ring in place - see what I did there?) and it's short enough so that it doesn't hit the wiring cavity.
If you don't want to fit a screw there at all, cut the head off the offending screw and glue it in place so that you haven't got the visual effect of a missing screw.
Last edited by Simon Barden; 13-10-2021 at 03:38 PM.