What's The Best Steel To Use ?

I agree with comments above that a repair is probably the most expedient. How did the second attempt at welding work out?
Using stock shafting would work fine (if it is available - what is it you need? LH or RH, 8, 10 or someother tpi?). How to check? Acme thread gauge. You could also roll it through some putty, then section the impression. Obviously you'd still have the collar and bearing area to sort out (still quite a bit of machining).

If it were me, I'd knuckle down and make it (seems I usually take the more difficult route - but less fooling around). You should be able to get by with out a follower rest. I'd suggest something really easy cutting. There are a few approaches you could take. Complete the Acme threaded end first (that leaves the "handle" in the chuck pretty stiff). Change to a dead center in the tailstock for the threading. Suggest you grind your threading tool too narrow, and cut each flank seperately (make the tool very keen and plenty of positive top rake) - this will reduce the deflection. Start by cutting the thread to the book values, then compare to your existing lead screw by measuring over wires (the size does not really matter, you'll just make the new one to measure the same as the old one). If you can get the nut off, the shaper - just cut to fit. The fit may tighten up slightly near the middle, but I doubt that will matter in your application.
 
I have made a lot in my career out of 12L15, machines and threads easily and has a great thread finish when single point threading.
 
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