Hinge pins twisted off - Now what do I do???

Definitely try to avoid breaking the casting at all costs. If there is room, I'd probably opt for drilling vs hammering, even if you need to get an extra long / aircraft drill bit and you may even need to drill the top out, then reach through that hole and drill the bottom. Might also consider an "easy-out" bolt extractor and doing all this in combination with the heat/blaster mentioned above if needed!

I had the same prob with a nice resolute model that some nitwit let sit outside for several years. Every nut, bolt and pin was frozen or broken. I would never have go it back in shape without my acetylne torch. It turned a nightmare into a dream. A propane torch may or may not have the heat but its worth a try. Next step up is a map gas unit. Just my 2 cents

pins need to go out bottom to top as they are a bit larger top side it isn't very much but if you try to force them down likely will break casting. Pins have small taper top to bottom so are a bit self adjusting as the area wears.

I had to remove pins on a resolute and when the pb and punch didnt work I went to propane... Little heat work the pins, little heat work the pins. I may have been more cautious than needed but I was concerned like you are with breaking the cast. I did eventually get them out at a rate of about an 1/8" at a time it seemed.

I wonder if you have a welder could you fabricate a screw press? Weld a nut to a piece of metal, like maybe half inch square stock, slip it over the ear and draw the bolt in from the bottom to put pressure on the pin, let it sit overnight soaked in PB then try a few more turns? That way you are applying constant even pressure to the cast vs a sharp blow.

As far as welding it.
A buddy of mine is a professional welder, according to him welding cast is easy, he told me the trick is to heat the whole piece that you are welding so you dont have a real hot spot that can cause further cracking in the cast. in this scenario in order to weld it his way, would be to remove the front panel of the stove, heat the entire piece to an even temp (exactly what temp I dont know) then do your weld, wrap it up to allow the entire piece to cool slowly at the same rate.

I've always just drilled through the pin at whatever angle I can with like a 1/8" bit, then try to drift out the remains. I actually have a 3/16" drift pin which I put a slight bend in for this very purpose. I haven't ever noticed that hinge pins are tapered, gonna check some new ones w/ the calipers tomorrow.

I'm SUCH a geek.

It isn't much of a taper, just a few thousandths