you could go about it a few different ways.
1 - tack it off from behind with cloth/t-shirt/fleece, then lay glass over top and behind.
2 - use cardboard to seal and glass over top
3 - thin(1/4") MDF wood tacked in a glassed
4 - cut the stock pocket pieces to fit and use those as a backing
no matter what you do, make sure to scuff the plastic good and drill a bunch of holes and glass frant and back to add strength and to make sure it wont pop out of the door as glass doesnt like to stick to plastic all that well.
