Chosen Solution

The upper screw which also holds the display assembly is stripped to the point that it’s basically round, similar to the bolted screws on the mainboard. The “rubber” / “glue” methods are out of the question. Do you have any real suggestions for me? I haven’t tried with a drill bit yet. Should I? If yes, which size?

Are you talking about the screw in step #9 of this guide? MacBook Pro 15" Unibody Mid 2012 AirPort/Bluetooth Board Replacement If so try using these: Screw Extracting Pliers