Does it exhibit the channel imbalance when playing tapes made previously, or only with stuff you are recording now (need to determine if it's in the record or playback signal path)?
Simple stuff not requiring test gear or soldering: try reversing the output leads and check to see if the problem follows the change; check the output volume control and tape monitor switch on the deck-they might be dirty. I assume you have checked the cables and receiver or preamp inputs (try different ones). It might also be a dirty tape monitor switch on the pre/receiver.
This is all simple and maybe insulting stuff (no insults intended), but I can't tell you how often I have missed the obvious and torn into things to find a simple cable or switch problem. I assume you have tried recording on more than one tape