Then I rolled the window down, and it was still pretty squeaky, and now I could see why. The roller on the regulator arm was all frozen on its little rusted axle. So I sprayed it like crazy with silicone spray.
After doing this, the window rolled up and down beautifully and quietly. So it was time to put things back together. You basically just do everything in reverse, except that once you have the plastic barrier in place and are putting the interior trim panel back, there are these 4 (or actually 5) holes in the top of the trim panel.
Those holes are there so that the padded trim up by the window opening can attach to this trim panel. There a thin metal tabs poking out of the bottom of that padded trim piece, and you bend those tabs straight with your fingers, poke them through these holes, and then reach behind this trim panel and bend those tabs over to hold the two trim pieces together.
I can't show you any of this, because the metal tabs are hidden from view, but you can feel them, and all this bending is done by sticking your arm back behind the panel and bending those tabs. After the tabs are attached, and you have fed the door handle back through the opening, then you can snap all those yellow snap connectors back into place.
The last thing to do, other than putting all the screws back in the armrest and interior handle, is to put this window crank handle and its finicky clip back into place. I used a putty knife again.
So that's pretty much it. The windows work perfectly again. I should have done this ages ago.