A strange thing as well one channel is much louder with the frequencies than the other. One is quiet enough that the music would cover the sound but the other is much too loud.
Big clue here, hinting the problem is a connection or routing and not shielding, and that at the very least you should be able to bring the level of the noisy one down to the level of the quiet channel.
Have you tried listening while moving wires, wiggling connections, moving components? Move one wire at a time, starting with the noisy one. Start where it goes into the phono stage. Listen while wiggling the RCA. Twist it. Slowly unplug it part way. Listen the whole time. Then listen while moving the interconnect. Work your way like this all the way back to the cartridge pins. Do the same with them. I recommend tweezers.
Cartridge clips by the way, if they are loose- pull and crimp. Very important- use a round toothpick to avoid crushing!
Was tracking this down with a friend one time, he picked up the phono stage to move it I said, "Freeze! Right there!" Turned out all he had to do was stand there holding it, I could hear music just fine. Seriously. It sounded real good. For some reason he kept on going looking for a better solution. Never could figure that one out. All he had to do was stand there holding it, I could hear just fine!
I tried moving around speaker cables and same thing.
No idea what this means. Your problem is somewhere between the cartridge and the phono stage output. Unless your turntable is on speaker cables I doubt they have anything to do with it.