Hi DD!
I think I may know what your issue might be! I have a set of 70's Premier snare drum lugs, with original Phillips-style screws. Upon closer inspection of the screws just now, I see that they are not Phillips, but a style called "Pozi". I have a set of both regular Phillips and Pozi-phillips bits. Here's a link that will be really helpful... https://www.finehomebuilding.com/2015/09/16/what-is-the-difference-screw-bits-phillips-vs-pozidriv
I feel that this is your issue. Are these Pozi bits available in your area? Also, it's very easy for a standard Phillips screwdriver head to render the Pozi depression unserviceable. This has happened to me and I've had excellent results in just using a small pliers to grasp the round head and loosen it.
Hope this all helps. Let us know!
-Mark