I recently bought a 1933/34 tail lamp stand like I am making, to replace the one on my car that went through my fire.
The lamp stand was off my car to be used as a pattern, the car was home.
The stand I bought had both bolts broken off with just a 1/8" or so sticking out of the mounting plate.
I have never had much luck with welding a nut onto broken studs, so I asked a friend up the alley, that repairs all sorts of old machinery, what he would do.
Usually if there is enough sticking up, I will heat the stud red hot and let it cool down 2 times. Then I use vice grips to turn it out. This hardly ever fails.
Since there wasn't eough left for that, my friend told me to throw away the nut I had brought along and he would show me what he does with broken off studs.
The bolt studs were 5/16 so he drilled a 5/16" hole in a piece of steel that was .060 thick, and a little over 1" long.
Placing it over the first stud, he welded it with his mig welder. It turned right out.
Same with the second one.
He said he quit trying to weld nuts on a long time ago.
I will try to post a couple pictures.