Excellent. Thank you.
A couple of notes here:
1. After you delete the superfluous backups in iTunes prefs, wait some minutes before creating new backups from your iDevices. Otherwise, iTunes will crash. No harm done-- just re-open and delete any remaining unwanted directories-- but time wasted. It seems like the backups immediately disappear from the iTunes prefs window, but actually it takes a few minutes for iTunes to actually finish erasing them.
2. I became aware of the large file using a free app called "Disk Inventory X," which provides a graphical representation of your drive(s) and really helps locate large directories on your drive. It is very good. Just be careful before deleting anything to make certain that you arent' deleting something crucial to system operation (the iNode directory, for instance).
3. Happy sailing, and thanks again to everybody on this discussion topic who contributed. I'm so pleased to have finally freed up some space. Saves me having to buy a larger SSD. Sweet!