Find a bolt where the screw part fits closely within the hole in the bolts. That will hold it in place. Plain steel, non galvanized (toxic fumes), non stainless. Weld it to the bolt head after cleaning any plating or finish there may be off with a flap wheel.
You don’t need a fancy or expensive welder. Something like this with flux-core wire should do. You don’t need pretty welds, just ones strong enough to remove the #%$^&ing bolt.
Adequate auto-dark helmet will run you $100 or so. Don’t bother with the theatre masks that you have to hold in your hand — they’re useless as well as needing three hands to use.
Practice with the two bolts you CAN remove clamped in a vise before going at the real thing. If that doesn’t work, you can always move to plan B, grind off the bolt, and drill out the rest.
