Hi Ed,
Usually scratches on the door glass are from using screws that are too long to hold the grab handle. The screws scratch the glass when the window is rolled up and down so they are vertical scratches/gouges. You said the scratches were in a line across the width of the glass? Both sides of the glass or both left and right windows have scratches?(if so, inside or outside?). When you pull the door panels you can inspect the window frame and regulator (try moving/shaking the parts sometimes welds break loose or bolts missing), alignment, window top seals/clips, etc. There might be part of the regulator that traces a horizontal path. There is no need for extra cushioning or rubber if everything is set up correctly.
Also, just a warning for anyone following this .. anytime window glass has deep scratches it should be replaced. Since it is tempered glass it is manufactured under pressure and with scratches the strength is compromised. One of mine literally exploded while stopped to fill up with gas. Luckily no one was injured.
Cheers,
John