Okay - so I'm thinking about this more, and since several people have suggested brazing, which requires less heat and won't spatter, I'm thinking that might be the better option.
Unfortunately, I'm completely out of garage space - which means buying a full size brazing rig is out of the question. (My stepfather has one, but he's 6 hours away, so that's a no-go as well).
Would something like
https://www.lowes.com/pd/BernzOmatic-Cutting-Welding-and-Brazing-Torch-Kit/50126405 work for what I need? I suspect I might need to buy an extra set of cylinders for it, so I could have plenty of time to practice. It looks like they recommend nickle-silver brazing rods for use with steel.