Making jacketed bullets out of free range brass is actually caveman simple to do and doesn't take a lot of $$$ in equipment. With nothing more than a rock chucker press and common reloading dies, cast bullets and push thru sizing dies. I can turn out jacketed bullets.
Take a little time and look in a book that have diagrams of the different shell cases and their dimensions. The 6mm & 244 Remington, 257 Roberts, 6.5mm x 257, 7.7mm Japanese all have .429" diameters at the shoulders of the cases. Any of those fl sizing dies can be used as a nose forming die. I use a 6mm/244rem fl sizing die simply because I don't want a wide flat nosed bullet.
Free range brass/ 40s&w brass tumble cleaned
For the lead cores I used a 41cal hbwc cast out of free range lead. Some of the different hbwc'sI cast.
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I don't have a 40s&w shell holder so I use a 38spl/357 shell holder instead.
Use a 41mag expander die to expand the 40s&w case.
Drop a cast bullet in the expanded case (.401" 40s&w bullet or a .410" 41mag bullet) I prefer the .410" cast bullet.
Use the rod that goes into the shell holder from a set of lee push thru sizing dies. I use a .429" set
Set the expanded case with the cast bullet core on it and screw the 6mm fl sizing die in the press and adjust the fl die up/down until you get the nose profile you want. As your forming the nose of the bullet the body of the 40s&w case will be swaged/compressed into the correct diameter and the lead core will compress tightly against the 40s&w case.
Take the newly formed bullet and run it thru the lee ..429" sizing die.
When I make hp jacketed bullets out of shell cases I use a cast hbwc bullet for the cores. I also use a set of Hornady blank dies to put "XTP" notches in the nose of the bullets. If you look at the jacketed bullets in the post above you will see 2 lines/rings in those bullets. Those are there from the lube grooves in the cast hbwc. That's how tightly the core compress/expand/grab those 40s&w cases. They make excellent crimp grooves.
Making the bullet was simple enough to do, making the cores stay intact was a lot harder. It took 4 or 5 tries with different alloys to find a core that didn't implode. Testing @ 25yds into wet pack with a 1100fps load that simulates a 75yd to 100yd velocity/hit.
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Anyway simple enough
clean the cases
expand the cases
drop a lead core (cast bullet) into the expanded case
Run the case/core up in a fl die and form the bullet
Run the formed bullet thru a .429" lee push thru sizing die.
Wash rinse repeat
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