I do stems the hard way @Kal. I cut the blank; turn it round; core with a long bit as true as possible; Then cure.
Then I come back and true the blank to the bore; square the ends and cut the VC port 10mm deep with a 3-jaw chuck.
Now the body is ready for shaping; I use a collet with a 5/16" stub against a live center on the tailstock.
I use a jewels lathe so some of this is geared towards that. I run a 4mm bore where a pen blank rod might be harder to do.
Thanks for sharing your method! I don't have collets, so I may just try and make my own bushings out of brass or HDPE.
Have you tried a stem with stabilized wood? I'm not sure how it would do with the heat, but using a brass tube inside the stem where the tip connects might be enough to keep it under the 372ºF cactus juice is rated for.