First, get the glass seperated from the regulator so you can manually move it up and down to see if it is hanging up somewhere. Right now you don't know if your problem is the glass getting stuck in the channels, or the regulator not functioning throught the complete range of motion. The glass will be attached to the regulator using 2 pinch clamps (metal with plastic or rubber on the glass interface). Any pinch clamps I have worked on were tightened and loosened by bolts (10 mm head on my Bonneville) but based on your description it sounds like yours are riveted. Undo both clamps and move the glass up and down. Even if it gets cocked, it should be fairly easy to straighten it and move it up and down.
If the glass moves freely, I would wedge it into the up position, and remove the regulator for inspection and repair. Last time I did this on my son'* F250, I cut 2 small wood wedges, and jammed them between the glass and the door trim to hold the glass in the up position.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)