@paulgardner This does not sound like a cartridge problem. You switched the leads and came up with nothing conclusive- this suggests the problem is something else.
The most likely problem is a tube. First identify the phono section tubes in your amp. Turn the amp off and swap the tubes that are the input to the phono section- this is where most of the gain is produced. Warm the amp up- did the problem move?
If yes you know the bad tube. If no, proceed to the next pair of tubes in the signal chain and perform the same procedure- continue this until the problem moves.
But- if you have a line level source like a CD player, try that. Does it have the channel imbalance? If no, the problem is only in the phono section. If yes, its not the phono at all. Perform the procedure above only starting with the preamp tubes at the line stage level. FWIW this could be power tubes as easily as any other tube so it will sound better when you get this sorted out.
Keep us informed- good luck.