(mackinaugh provides some addtional information for fixing loose windows in their tracks.)

Thanks a million to rob13572468, ace3 and Stan. After a late night a work, I came home and tore into it again. Here's what I found:

  • There are 3 screws that can be loosened to adjust the window left-right (from the side-of-the-door perspective).
  • There are 2 screws that can be loosened to adjust the window's slant left-right (again, looking at the door from the side).
  • There are some white window-stop things on the window. I believe the topmost window-stop thing on the rear of the window was part of my problem. I think it was hitting a part of the door, but I can't be absolutely certain because it's really hard to see what's going on all the way up there through the smallish hole.
  • There are holes in the bottom of the door. This doesn't really have much to do with the problem OR the solution, but I noticed them and thought it might come in useful for somebody. I was able to position my flashlight in such a manner as to shine through the holes so that I could better see what was going on in there.
  • The rear rail has a screw on the top of it that can be accessed from the top. It doesn't seem to adjust anything, but if it's loose it will cause you grief.

The rear screw of the 3 that need to be loosened in order to adjust the window towards the rear of the car.

The middle of the 3 screws, circled in red. The 2 screws circled in green can adjust the window's tilt.

The front screw of the 3. You can see it hiding behind the door-handle-assembly-thing (can you tell I've never done this?). I almost turned back here, because I didn't think I could get to it. Right under the screw you can see the bar that runs from the handle back to the door latch. I lowered the window so that the screw was just under that bar, and got to it that way with some extensions on the ratchet. There's a U-shape carved in the black piece that you can see in the picture; that's where I lined it up.

You can also see in this picture that I took the window controller off of the door panel so that I could operate the window without having that huge panel in the way of everything I was trying to do. It's only 2 screws.

The window-stop things.

The screw that holds the rear rail to the door. This is what I had to tighten to fix my problem.