Further testing shows that two welders do, indeed, work. As does three makeshift welders.
One welder and two makeshift welders, however, does not work. Nor does one welder and one makeshift (with the makeshift one being the charged one).
Two welders and three makeshift welders also work.
It would seem that you need one more than the recipe requires of any and all welder variations you have at hand, which is rather a different bug than it seemed to be.