They sent us a video on how to remove it with "tools". That consisted of a picture of razor blade scrapers of varying lengths. Trust me, those would not work. All I know is the amount of labor trying to remove it. You might as well just buy a new door.
My first thought when I first saw your predicament.... "I think I would have just left it alone"
EDC an MC acrylic cement are used in the plexiglass manufacturing. It is more like an aromatic light solvent than a glue. We dispense it using a needle tipped bottle and it evaporates about the same speed as 90% alcohol.
Now it will 'fog' clear plexiglass surface, but if you could carefully place a drip on the crack, it would have quickly ran the full length due to capillary action and 'welded' the crack shut.
It would likely still be visible, and it would be sealed (if the two halves were tight enough to begin with) There are also acrylic cements that contain the EDC or MC solvent but they are additionally thickened with additional acrylic that has been dissolved for filling larger gaps.
I think that the plastic window is going to 'part of the structure' so consider re-installing the door, insert the window, and with the sealant adhesive still uncured, make sure that the door takes its set and the seal and shape are correct.
Now as I type this, I envision removing the door frame weather sealant so it shapes without the additional pressure of soft spongy rubber and then after it is all cured back up, reinstall the weather stripping... There are so many techniques and variables, it is hard to imagine all the aspects of the situation without actually being hands on...
Bon Chance!
Tecnamech, please let us know how it all turns out when complete. Show us pictures of the outcome and give us your "lessons learned" from experience.