AMC Record Player Crazy Loud Humming

Those 50C5 tubes were used in old electronic designs that used series heaters directly run from the AC mains and can be extremely dangerous. My understanding is that some of the transformerless designs could have a live chassis! You're asking for trouble modifying anything in there.

Sorry! I'm at a loss.

Would there be any easy way to test this though?

This is what I originally thought but could not find a ground wire or a hook up for the ground wire on the back panel. However what I am pretty sure to be the ground wire, running from the phono to the receiver, I detached and reconnected it to a different part of the TT and still got nothing. But all in all could not find an obvious grounding “screw” which I thought was weird. 

There ought to be a simple Grounding Wire emanating from either the tonearm or the turntable. Screw the wire onto/into the receiver or phono stage's grounding screw...which should be on the back panel. With any luck, silence will instantly prevail.