You got a drill press with a table vise?
Clamp the barrel in the padded vise. Chuck a length of screw that fits the stud, 1/4"x20, I think. Screw the stud onto the screw and adjust things so that the stud comes down exactly where it broke off. Without moving anything, clean and flux the barrel and the stud. Slide a short length of something like Brownell's Hi-Force 44 up into the stud, bring down the quill to press the stud in place, and hang a weight on the press arm to keep it there. Then all you need to do is heat until you see solder flow.
You have to do the setup before you do the cleanup so you can see just where the stud fits. If you can get a current stud, do the setup with the old stud, and then replace the old stud with the new one on the screw. The new studs have a base to give more soldering area because the old ones were real bad about breaking off.