OK So another update:
I DID have this radio working fine last night, but then when I went to install a permanent power cord onto it tonight (instead of the temporary one I had on last night for testing purposes) I went to fire the radio up after installing the new permanent power cord and wouldn't you know it the radio went back to humming like a son of a gun again!
I checked all of the ground connections and they were fine, I checked all of the electrolytics and they were fine, and I even checked the 6J7 tube's Grid Cap wire shielding and that was fine so I don't know what to say about this thing!
Any ideas as to what to check next? Because I'm starting to run fresh out of ideas on this thing...