You're a braver man than I am, Gunga Din.
Like Keepaeyeonit said (I think)...When I clean my stove glass I have a triple-thick blanket of heavy-duty aluminum foil (I get the wide roll) that I shape to the raised rim around the door opening, where the gasket seals when the door is closed, and just let the fire burn. If I had to do a door repair while burning, I'd likely do the same thing.
You can fasten the foil on with a couple of those small metal spring clamps used for gluing, but on my stove it stays pretty secure just by friction as long as you pinch it pretty good all around the door rim--wearing gloves, of course.
I have a CO detector right next to the stove and it's never peeped, even when I've taken my good old time cleaning the glass.