My .22 K-Hornet is a different beast, but taught me a lot about managing that little cartridge. It's a 1935-vintage Winchester M54 .22 Hornet converted to K-Hornet by Lyle Kilbourn himself (the "K" in K-Hornet).
My protocol for eliminating split cases upon fireforming is to not fireform the brass at all. I utilize a hydraulic case forming die from Hornady. Without going into a lot of detail it involves water and a big lead hammer. Annealing the virgin brass first is important also. It produces a nicely formed case with plenty of shoulder to headspace on for initial firing, albeit with the shoulder corner angles left a little soft. (Not that that's really critical in my instance as this rifle enjoys headspace as tight as can be.) Initial firing then sharpens up the angles crisply. I haven't lost a case yet, and brass lasts a loooong time- the chief virtue of the K design IMO.
I've often said that if limited to but three rifles, please let one of them be a Hornet.