After considering the options and my abilities, I decided to widen the thread gutter and use the tool I just ground out of 1/2" HSS. The 60 degree threads went fine, it was beautiful really.
Unfortunately for me, I neglected to retime the Acme thread to the vee thread. So the cut wasn't in the center of the vee. This fact simply slipped my mind. But I finished the thread, warts and all and tried it on the broom head. I found the threaded section was a little long so I faced off a whole thread. Now it screws in all the way, hiding the messed up threads.
My previous piece, I had retimed the threads, or I was extraordinarily lucky. I'd like to think it was skill though.
I'm going to redo it, but after I finish the piece. Might as well make some more mistakes on this "test piece"! Have to drill out the handle side to fit the existing handle. It's 7/8" in diameter.
This project is definitely motivating me to think about my ELS and adding in the feature of thread to stop. I've thought through the basics now and know what I need to do, at least for imperial threads on an imperial lead screw. For metric, I have a glimmer of an idea, but only a glimmer. If I could control the spindle motor, I can do it. Otherwise, it remains a tough problem.