I too swage .223 bullets from lead cores & spent .22 LR cases.
I have a set of Corbin tools that I bought second hand & a CH cannalure tool. My Corbin tools were a set,, and came with an ejector adapter which makes a big difference in how easy it can be to push out a bullet during it's process. Most types use a punch & hammer as the ejector. I got lucky in buying my stuff.
You can cast lead cores,, or buy lead wire & a wire core cutter. I made a lead wire cutter myself.
As noted,, the tools needed aren't cheap,, but you can do it. And if your make enough bullets,, you can eventually recoup your expenses.
I use a RCBS Rock Chucker press as well. In fact,, RCBS actually stands for; "Rock Chuck Bullet Swage" press. That's a bit of history behind the RCBS brand.
Oh,, you can also swage jacketed bullets using lead cores,, and spent pistol brass. .9mm brass makes good .40 cal bullets,, and .40 cal brass can make .44 or .45 bullets easily.
As mentioned,, over on the cast boolits forum,,, there's a section on swaging.