Actually the square collets are the nicest.

Centering small square stock in the 4 jaw is a pain. With my lathe I can freely switch from 3 Jaw chuck, 4 Jaw chuck and two different kinds of collet systems. Whatever is best for the job.
Yes, turning the stem as you describe isn't that hard as long as you have a decent die holder for making those tiny threads at the end. The biggest change from the plans is they use an o-ring for sealing the valve turny-bits assembly that screws into the valve body.