You didn't mention whether the car is still together and painted or if the body is being prepped during restoration. If the former, judging by your Avatar photo, I'd be leery of using any kind of flame to braze or weld the holes shut. Remember: the gas tank is only inches away from the lower stanchion stub. Ruined paint at the least could occur, a gas tank fire/explosion at the worst.
Five years ago my '28 Phaeton was experiencing a loose right side windshield post. The threads on the stub were stripping due to age, so the bolts couldn't get a tight enough grip to secure the posts from leaning to the back. It's different than your '30-31 open car's shorter, lower windshield stanchions, but the threaded stubs underneath are the same. Rather than risk ruined paint or a fire using a flame, I reached for my tried-and-true repair epoxy that has saved me many times where welding or brazing was not practical. It's called SteelStik, made by JB Weld. It's a two-part epoxy that you mix together and then knead between your palms until the color is a uniform dark-grey. Apply it quickly because it starts hardening in a minute or so, depending upon the ambient temperature. To fix my problem, I removed the tall right side windshield post, cleaned out the two thread holes with acrylic lacquer thinner, and followed that by running a small, stiff wire brush through the holes so that the epoxy would have a good, clean area to grab onto. I rolled a ball of the SteelStik and worked it into the two holes, like working with clay, filling the holes completely, then smoothing both sides so that there would be less to trim away after the stuff had cured. It sets up in a couple hours, but cures in 24 hours. This stuff is TOUGH! You can drill and tap it once cured and it will not crack and break apart under stress like regular JB Weld will do. After curing, I sanded the outer area flush so that I could see the circular hole now filled with epoxy. This allowed me to find dead center so that I could drill the hole and then tap it for the slotted post bolts. There is a little play in the lower post/tall post holes created by the slightly larger holes than the bolts and the countersunk edges. So, even if you are a tad off center in your drilling and tapping, the bolts will bring the post into the correct alignment needed.
This stuff isn't terribly expensive and has a million applications afterwards. Try it. If it works like mine has for the past few years, your problem is solved easily and cheaply. If not, you're no worse off than you are now. Then consider the other suggestions offered so far - but be careful if you resort to a flame! Below is a link to this epoxy.
Marshall
https://www.amazon.com/J-B-Weld-8267-SteelStik-Reinforced/dp/B00RN7CT2U/?tag=atomicindus08-20
