Just an observation but for best wear you really don't want the nut to be the same material as the threaded rod, it will accelerate wear, that is why they usually use a bronze nut on a steel thread. Might not be an issue for something like a vice, especially for occasional use, but something to bear in mind.
Also need to think about how you mount it. If the vice body is cast iron then welding a steel nut to it really isn't a good idea, very unlikely that the resultant weld will withstand the forces involved. You would be better off to try and mount it in the same way as the original part. The normal type of vice nut is usually a square or oblong threaded section with a round stub bolted into the vice body. In that case you could get a suitable sized rod welded onto an acme nut, then machined to replicate the original part and bolt it in.
