OK, Here's some more information.
A. The regulator looks like this:
B. As you can see from this image, the motor bolts to the regulator on the funny looking structure attached to one of these 'scissor arms', and the motor then engages the regulator via a toothed gear. Then other 'scissor arm' attaches to the bottom of the window itself. When the motor turns, the gear moves one arm up or down, effectively it 'scissors' this structure up or down, dragging the window with it.
C. It's still possible that the gear is simply slipped off the regulator gear-teeth, or otherwise jammed because of dirt or foreign object. It's also possible that the window is out of it's side channels, or a channels is munged. But from what I can see -- which is not much, these look fine.
D. You can buy regulators for $50 off the net at a number of places. Like
This place for instance. Motors are closer to $80, so it sounds like you are getting a pretty good deal.
E. Since the regulator and motor are effectively bolted together with the six rivets you described above (and cleary visible attachment points on the regulator image above), there's no reason not to take the whole shebang out and test en masse. Especially since you have to drill out the rivets to remove either the regulator OR the motor. I figure to simple use bolts with lock-nuts to re-secure that assembly.
F. Oh, and my stuck window is the
front passenger window, not the rear; so your experience will be mighty helpful to me. In particular, how -- exactly -- is the window attached to the regulator? If I can de-attach the regulator from the window, I can slide the window up. This will give me enough room work on the motor/regulator. There are some small cut-outs in the bottom of the door that may allow this to be done, if I know what to look for.
Anyway, let me know what you find tomorrow.