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Glass and paint borders are a nightmare. I've always managed to crack at least one pane of glass stripping with a butane torch or heat gun. Now I use aluminium duct tape on a piece of cardboard or stuck to the glass which is works for infra red. If you are looking to get the mouldings really clean I recommend cloth sand 'paper', there's a type (can't remember the name) which I swear by, the soft pads in an few grits 80 - 180 are useful too but they wear out fast.
Tape the glass with a decent masking tape to avoid scratching the glass all round the mouldings. Use a tungsten carbide scraper (very useful for all types of work), there are also moulding scraper sets.
At least when I diy they're my mistakes. This whole process of getting people in to do stuff is one I hate, I procrastinated about getting the repointing done for fucking ages worrying about it being done properly.
Right now back to the door frame...