FYI 
I think you can make it with your standard 222 Remington die from 357 maximum brass.  When he was alive, Kurt Hardcastle was building rifles on small Martini actions.  The neck ends up shorter than a standard 222, about the same length as a . 223 neck. Kurt had a custom reamer made specifically for that short neck but I suspect this would work fine for your needs.
I'm not sure if he annealed them 1st but I suspect he did. 
Scott