Finally got rid of the blower fan problem!
I went to my parents to pick up my kids, and when I got there, my dad reminded me about a similar problem he had with his '95 Lumina APV. For a few weeks, he had to lightly tap his blower motor with a small hammer to get it started, the motor had developed something like a "dead spot" and could not start by itself.
So we tried that with mine, and you guessed it, it worked. So I removed the motor from the heater assembly (easy thing) and bought one from a local junk yard (a nice green '96 Mystique that seemed to have had an encounter with a train or something as ferocious).
Now everything works nicely, and the fan is much quieter than it was before... So I suppose the motor had been giving me tell-tale signs of it's oncoming death...
Horseydug - as usual, your troubleshooting skills have been immensely helpful! Thanks a million times (again).