Naptali and all:
Lyman used to (about 20 years ago) offer two-piece bullet molds for doing exactly what you propose: Cast a soft-lead nose, and a hard-lead base. the two pieces were them swaged together into one integrated unit, sized, lubricated, and loaded.
The nose portion had a "tang" that fit closely into the base portion that had a "socket", and on swaging together, were securely held.
I dunno if they still offer it in their custom bullet mold line, but you can certainly ask!
I would hazard a guess that at today's machine shop prices, you are looking at probably $100 to $150 minimum to machine those mold blocks from some old mold blocks. Even more, if the machinist had to make his own blocks to start with.
HTH
John