Advice on turning a custom tap

If you are running the work in a collet or in a chuck it helps to have a shoulder on the shank so the work can't push back.
I cut a 4 pitch Acme on a 1940s Pratt & Whitney lathe with no trouble using HSS tooling. I don't know the south Bend model you have but I suspect it should have the balls to do it. Instead of roughing the thread with a V tool consider first cutting a square thread then going in with the 32* tool.
A 6 pitch tap of that diameter is going to be a bear to turn. Have you considered making serial taps?
I have made threading tools with positive rake on the leading edge. It cut much better than a flat top tool.
 
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