And that will be best done with a rosebud (ideal) or large diameter tip in an O/A torch. That will require about 1100 to 1200 F degrees of part heating. Use a high-silver-content silver solder on the order of 55%. The screw rod would fail in tension befor the silver soldered joint would fail if properly done. To answer the OP's question about how strong silver solder is: In this application extremely strong.

It is just to illustrate the overall idea of the part assembly. The knob drawing is final but the acme threads in the assembly drawings is not to size or scale. And feel free to critique my drawing while you're at it. I'm looking for input, alternatives, advice, anything. Also the price would be much higher for the stock material required. I know it could be done as a single piece to avoid welding but I am a complete amateur on the lathe and wouldn't know where to being on cutting threads. 5 diameter and insert into the mating end of the 'knob' as means of concentric fixturing for the welding, and then back to the lathe to clean the face of welding buildup. I've drawn my own lead screw 'knob' modeled after the old Athol/Starret bench vises and my idea is to weld a piece of 3/4-6 ACME threaded rod on the knob.

The thread pitch of the all-thread is too fine and requires too many revolutions to get any linear travel, not to mention it was kind of a bang up job. As it came it had a make-do lead screw which was just a piece of all-thread and a nut welded on the end(see original pictures). I've acquired an old Prentiss bench vise that is missing the lead screw, or at least the original.

Assembly drawing of bench vice