Broken bolt removal: nuclear options?

Welp I did it!
Plan A was weld a nut: Got a great weld.....unfortunately the nut fell off at some point and not noticing it , welded the broken bolt to the "bracket"...FK!

On to plan B: I have a handful of carbide rotary files which I used to grind the top of the bolt so I could center a drill bit and hopefully (possibly) break through the hard part and maybe get to softer metal.....Nope. Regular bits still wouldn't touch it but I did manage to make a perfectly centered divot.

Plan C: Called the local Napa and they have cobalt and carbide drill bits in stock, yay. $25 later I'm the proud owner of a 1/8 cobalt bit and a 11/32 cobalt drill bit. Expensive Hole. Well the 1/8 bit got only so far before it wouldn't cut and I pushed it real good ;) and it broke. FK! To use or not to use (the 11/32 bit), not if i can help it. Using a combination of regular bits and rotary files I got the hole most of the way through, like to within 3/16 of going through so I cut the bottom part of the bolt that was sticking out and viola, daylight! I was able to finish the hole with a regular bit, ran a tap through and tried a 10mm x 1.5 bolt, it was loose so next and final step will be to go the next size up, either metric or standard.

So it took me about three hours of total PITA but it's done and it only cost me $6 as I'm returning the other unused bit.
 
Do I cut the “nut“ off flush with the bracket and then weld another nut in its place? Anyone have any experience with this particular bolt and found a solution?

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Still an option if the threading doesnt work. Looks pretty thin to begin with. You don't even need to weld a nut since there is access down there, just use a regular nut and put a wrench on it. Or drill all the way through to get rid of whats left and do the same - nut and bolt.
 
Using a left-handed drill bit, slowly a brad point drill bit a pilot hole.
Check the table on your extraction pack to choose the legitimate estimated left-given bore (likewise called a "converse boring apparatus") to make a pilot opening in this messed-up bolt. Left-handed drill bits, on the other hand, have a thread that runs counterclockwise, in contrast to right-handed drill bits, which are shaped like clockwork. This gives a superior nibble when you utilize your drill backward to eliminate a clasp.

Domo arigato, Mr. Roboto…