Well, I would like to summarize where things stand on this crazy project.
Wrapping the screw turned out to be a bust. It was just too hard to control motion of 3/16 stock on a 1.5 inch shaft, with uneven heating. One of the things we did try was to heat in a muffle, and maybe there was some impatience as the part was so big it was really hard to bring everything up to an even temperature in a reasonable period of time. Fast forward to compromise #1: machine the screw with a square thread, and then wrap it with keystock, remove the spiral and braze/weld it into a piece of pipe to make the screwbox.
Machining the screw, no problem. But things got a bit doomed when I did the math. The screw was cut on a lathe with 4 turns per inch (the lowest available). With 4 tpi and square threads, I needed to use 1/8 keystock. So I wrapped the thread and it became especially clear that brazing this in a forge was going to be messy and the bitty little threads would likely get fouled so..trying an idea my mentor successfully used for a larger thread box, I took the pipe and milled slots in it and tried to MIG the thing together from the outside of the pipe. Too small, too much spatter. Then I tried TIG. That would have worked better if I actually had some experience with TIG :). So by this time I had evolved pretty darn far away from anything remotely resembling a traditional method. Compromise #2: The other day I went into the machine shop, bored out a piece of 2" steel, ground some cutters for a square internal thread and turned the screw box.
I have learned quite a bit about the thermal properties of steel and techniques and strategies for fabrication over the course of the project. But no payoff in terms of the goal. I will come back to it, and when I do, I will restart this thread! In the meantime, this weekend I will continue working on my franken post vise, which has one heck of a screw and screwbox, made in the modern way. Thanks again for everyone's comments, suggestions, interest and especially encouragement.
Nicole