While I fully understand the desire to salvage the display Apple doesn’t make it easy ;-{
The cover glass is not just a plan sheet of glass it is masked off with a painted on bezel rim to hide the light leakage from the displays backlight. So while it maybe possible to cut the glass to the correct shape to fit smoothly around the edge getting the proper baked on enamel paint at the correct thickness will be tricky!
In the end we found it just too much work to hobble things back together at least we had a bad display to steal the cover glass.
And as you discovered the foam seal Apple uses makes a mess when you try cleaning it off. We never was able to clean it without leaving streaks and if you press to hard you also leave artifacts in the displays image.