First, have you looked at the sound control center in Windows to make sure the balance is set to the middle?  (Just asking the obvious first.)

One thing you haven't told us....

It's fair to assume the records are professionally produced.  Are the cassettes commercially made or are they home-made?  How many of the reel-to-reel tapes are home-made?  Do the commercially made records and tapes play in a balanced manner?

The brand of the equipment is largely irrelevent.  The question is whether it is quality equipment that's been properly calibrated.

We're assuming the recordings were engineered in "perfect balance" to begin with.  Some older recordings were mixed differently than the "modern" standard.  Sometimes the bass would be panned hard left and the guitar hard right, for instance.  This could give some people unaccustomed to this the feeling that it's out of balance.  If that's not the case, it's likely an equipment adjustment problem.

The anti-skate must be properly adjusted on any turntable for it to properly reproduce a balanced signal.  In the same vein, the play head on any tape player must be properly aligned to produce a balanced signal.  If playing a mono tape on a mis-aligned stereo tape head, the results will be an out-of-balance sound stage.

In the case of home-made tapes, you may have a situation where the tapes are played on a different machine than they were recorded on.  One or both of the record/ play heads on the tape machines (recording and playback) were/are possibly out of alignment.  In this case you may get all sorts of varying results.  The best way to solve this problem is to properly align the playback head on the tape machine for each tape that you are playing.  Obviously, this may be difficult or impossible, in which case adjusting the balance in your software may be the only solution.

Obviously, in this day and age of digitized music and MP3 players, the old "Hi-Fi" technology is becoming a lost art.