If you can find someone who can cobble together a bump die that could be your trick (aside from paper patching). I made one but haven't tested the slugs as of yet. It took a .357 to .367 and in the case of the lube grooves they stay intact. It was able to do the same with jacketed bullets as well.
Just another way to approach the problem.

I just found a drilling that may be in the same chambering as yours so I will certainly be looking back to your post when I approach mine.

Looking forward to your results.

Tom

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