It wouldn't hurt to play around with some 40s& w cases. They make excellent bullet jackets for the 44mag. A couple years ago I did a little testing using them to make 44cal bullets for the 44spl/mag. The main thrust was to make a hunting hp for the 44mag. This is what I ended up with.
https://i.imgur.com/QOZKxm4.jpg?2
While testing I did make up some jacketed hbwc's using 9mm cases for .357" bullets and the 40s&w cases for .429" bullets. With the 40s&w brass I made a custom expander and opened them up. Then I used plumber's flux and a cast bullet for a core. Put the expanded case with the flux/lead bullet (core) into a cast iron skillet (+/- 200 of them) and put the pan in the gas grill and turned it on high and shut the lid. +/- 10 minutes later the cores and melted. Shut the grill off and let everything air cooled. The end result was a jacketed hbwc with a bonded core. I ran those hbwc's thru a lee .429" sizing die for the final sizing.
The end result was a jacketed hbwc bullet that could be loaded/shot traditionally in the 44cal's. It was an excellent type III hbwc with the actual base of the 40s&w case smaller then the diameter off the bullet (tapered nose). They could also be turned around and used as a huge hp/cookie cutter. I was mainly interested in the huge jacketed cookie cutter hp and tested them in a snubnosed charter arms revolver. These are the 44psl bullets I tested included the jacketed hbwc's.
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https://i.imgur.com/xcnl3kR.jpg[/IMG]
This is what the recovered bonded cored hbwc's looked like, noth the 38spl & 44spl hbwc's were shot in snubnosed revolvers.
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https://i.imgur.com/ssPg90t.jpg[/IMG]
Did a little testing with screwing hardened screws into the flash holes on the 40s&w cases (panhead & hex head) and then bonded the cores. Also put the screws in from the inside so that the threads were sticking out the base of the 44s&w case and then bonded the cores locking everything together. I can only say these bullets were extremely impressive/destructive in hot 44mag loads in a 6 1/2" bbl'd 629 and a 10" contender.
Actually it would be cave man simple to turn down some O1 to whatever shape/design you want. Then press fit the 01 core into a 40s&w case. I'm sure that bullet would do what you're trying to accomplish.