First thing is I have no experience with swaging. Second, If this is a stupid idea, no harm, no foul. I wonder if I could cut steel cores for .224 bullets with a precision micro cut off saw. Steel wire is available in almost unlimited sizes and I think if I were to cut a steel core the right diameter I could actually use it for a de riming punch that stayed in the case. See what I mean? put the steel core in the 22 lr case and push it through a Lee .224 sizer die. The steel core would then be seated and the case de rimmed. Then a fellow could run the jacket/ core through a point former and be done.
A couple of problems I see are "spring back" I know sometimes with copper/ brass etc you have to size a tad smaller because of spring back.
Some are probably wondering why a steel core. Several reasons. first, it would be cheaper and easier. As I say, steel is available in almost infinite wire size. Second, it would get higher velocity, and penetrate better. I wonder if a pellet of lead could be inserted in the nose before forming? Very similar to a Fail Safe then. The nose would expand, and the steel core would penetrate like nobody's business. If good bullets can be made this way it would be much faster and cheaper, skipping several steps. Lastly, it would give the .223 some penetrating ability. I know someone will bring up the "armor piercing " boogey man, but 62 grain green tips have a steel core. No problem buying them. Or at least their wasn't until the latest ammo scare.