I don't see any comments about your use of any kind of penetrating lubricant on this. Have you done anything like that?
Kroil is my first choice, and that well in advance of working on the parts. Hit both sides tonight and let it set until tomorrow. If you don't have Kroil then use 50/50 acetone and ATF.
The next step is heat. Yes, keep a bucket of water and a fire extinguisher handy. The penetrant will burn, but it will burn off pretty quickly too.
I trick that I have not tried myself but have heard people swear by is to heat things up and then melt a candle on the hot metal. Even a candle from a birthday cake will do. I would be inclined to try this on your broken stub of a bolt.
After you have applied penetrant and heat and a candle then see if you can't get that thing to move with vise grips.
1/2" worth of stub probably isn't enough for a pipe wrench, but perhaps if you could get your hands on a fairly small one it might be able to get a clean bite on the bolt. Add a little leverage and see if that doesn't get it moving. The nice thing about a pipe wrench is that it tightens its grip as you apply pressure. If you can get a bite it could be the ticket to success.
Another tool that tightens its grip as you apply pressure is a set of Knipex channel locks:
https://www.amazon.com/Knipex-87013...rd_wg=Gmpt5&psc=1&refRID=GM7237VVXFJYP91Y64KB
I have seen those at Lowe's, so you might be able to source them locally. They are very well designed and might have a better chance of getting a bite than a pipe wrench. On the down side, they depend a bit more on the strength of your grip and you can't really add any leverage to them. However, once they do bite they really bite in with additional pressure.
If none of that works then I think you are looking for a local welder. I would not try grinding any of the stub away. You are going to need all of it you can keep.
Another detail, if you do manage to get it moving do not try to unscrew it straight out. Get it to back out 1/8 of a turn and then turn it back in 1/8 of a turn. Then get it to back out 1/4 turn and then turn it back in 1/8 of a turn. Then get it to back out 1/2 turn and then turn it back in 1/4 turn. Continue with that pattern. Treat it as if you were cutting new threads. You have a bunch of rust in there and no flutes in which to clear it out. Take your time letting those threads try to clear themselves as you work it out.