The basic process:
1. Clean the range pick-up .40 S&W brass.
2. Trim the cases to length (.810" for 275 gr bullets and .700" for 250s).
3. Expand the case mouth to .44 caliber (Lyman M die).
4. Match a lead core (lead wire or cast lead bullet - .40 or .41 cal) to the jacket, to achieve the desired weight.
4.a. If bonding, the inside of the case is fluxed, the core placed back inside, then the assembly heated. When the lead has melted, the flux stops boiling, and carbon stops bubbling up out of the primer, it is allowed to cool. If it "sinks" in the middle, it is bonded. If not, you've got some rejects. They look terrible, but work well. (5th photo)
5. Seat the core in the jacket by running the inverted assembly into a 7x57mm sizing die, on top of a Lee "pusher" (bottom punch) from a .430" push-through sizing die. This bevels the rim (side effect of the process), and "bumps up" the body diameter to about .434" by sealing the punch against the case body and expanding the lead core. (Second and third photos.)
6. Turn the bullet over, and run it into the 7x57mm sizing die to form the nose. (4th photo)
7. Lastly, lube the bullets and run them through a [bullet] sizing die.
Notes:
The primers are untouched, and left in the cases.
Tarnish doesn't matter.
I use pure lead for the cores. The lead wire is from RotoMetals, and won't be used again. (It is expensive.) The cast lead bullets are from Lee molds, 401-175-TC and 410-195-SWC. (In pure lead, they drop heavy.)
The bullets are ejected from the sizing die with a section of O-1 drill rod. Initially, I was using a letter-size rod that was about .186". But, I recently went to some N-size, that mics .297". It fits much better, and produces much better looking bullet noses. (last photo shows the .186")
I use a Lee .430" bullet sizing die, so the bullet's spring-back gives me a finished product at .4315" to fit my .432" bore better than factory bullets.