Wow what a story!!

Nitro, I wouldn't be surprised if .323 bullets do just fine.

Our Husqvarna 9.3x57's were commonly overbore and a lot more than that, some running .369-.370. IIRC, one of Daryl's is .370 if I remember correctly. Mine weren't that big, but were overbore
at .368 and shot just fine with .366 diameter bullets.

I'll lay a wager that some long-bearing .323 200-220-ish slugs will make the trip just fine and really, probably some 180's, too.

At any rate, as Daryl says, 2 or three dies from LEE should fix you up. We take led-core .375 cal bullets all the way down to .366-.368 and have no problems and excellent accuracy.