Chris, have you ever thought of swaging down a 375 Winchester bullet ?
Many years ago I took a 200gn, can't remember if it was a Speer or Hornady, soft point jacketed bullet and after a lot of grunting resized it through my 366 push through sizing die.
I only made the one as my little RCBS JR press nearly gave up the ghost with the force needed ! being a flat nosed soft point it allowed the surplus lead to extrude out of the top. I have sent you a pic of the assembled round by email - I never fired it but kept it as a souvenir.
I'm sure with a bigger press and an interim sizing die you could easily make and try a variety of different size and shape bullets. I can't attest for the accuracy of the bullet with this process but the one I made looked good.
Nick