It would allow removal of the glass but I would still have to remove the remains of the screw.
-A far easier task with the glass out, less risk of shattering the glass than any of the hammer driven solutions mentioned. The head often presents the problem of rounding the socket, an 1/8" hex in an already shallow button head is no surprise either. Once the head is removed the "lock" is often gone and the remainder of the threaded portion can be easily removed unless it's corroded/oxidized in place, a wood stove door will do that with the heat cycling. If the fasteners are indeed corroded then you may very well have to face removing the threaded portion anyway. That's not a real big deal either IMO.
If it is case hardened I could drill out the center but seems like it would be a real pain getting the remains of the threads out.
-Maybe but maybe not. Extended soaking in a something like PB Blaster or Liquid Wrench could loosen the corrosion enough for easy removal, many here have done this. With the glass out there's several options. If chemicals don't work you could always heat the fasteners to red hot, this will anneal (soften) them. The heat alone may break the corrosion loose enough for removal. If this is too much of a "pain" then do as you wish to and as you are capable of.
-If this is just a simple repaint of the door why not mask off the glass and repaint? This will avoid the difficulty of the fasteners. Good luck.