[Arran]

I can see one reason that the spider may have been buzzing, where is the washer that goes under that center screw? I've never seen a 45 RPM adapter style spider that did not have a washer under that screw. If it's missing the screw may have bottomed out and the spider may be just slightly loose in the vertical direction. Even if it isn't loose there should still be a flat washer under that center screw to spread out the pressure, otherwise it may work it's way through that thin cardboard with use.
Regards
Arran