This is a bit silly but keeps you off the streets. O.K. the .222 family is about .373 in the body at the base. So you propose to cut off the die to resize --.222 family... .221, .222, .223, .222 Mag or the TCUs-- so a .375 bullet will slip into the die WELL LUBED, lanolin and castor oil or a mix is the "old standard" and come out the top... .366.
Can you do it? Probably. Hard work? HARD WORK for a Rockchucker Press? Yes. Love mine but this is not what it is designed for. Rock Chucker Bullet Swage (s) made .224s with rimfire brass for cases. If you do many, that press may retire long before you planned. Please lube it well.
Basically you need a machinist with exceptional measuring skills. Or buy up a half dozen dies used at a gun show and go "back yard bubba." Neck will be in the area of .224 + .0015 + .0015 (neck thickness), maybe .227 outside and you want to cut it off in the shoulder in the neighborhood of .366. Look up the diagram in a reloading book. I would want to go in steps. .375 to .370 or so. .370 to .368. .368 to .366 or .3665... You will find the bullet core protruding...
Mr. Dave Corbin has his books posted on his web site without pictures. He does this with 8mm bullets, .323 to .318. Quite a squirt of lead coming out the swaged down bullet.
So you cut the first used die off with a carbide hack saw or
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Probably hardened inside anyway. Lube a bullet. Shove it thru? Mike the bullet. .370 or plus? Cut another die a bit shorter... Try again...
Yes, this is a lot of "bubba work." Fast and cheap you go to a machinist and have them make you, Mr. Corbin calls them "ring dies" to do each step... or a real, long tapered die with a long punch... Might have synthetic lubes to sell you too. Core? You have to decide. You push it back rounded over or clip it off. More "die work."
The alternative is to buy a LEE size die, probably custom order, in .366 and WELL LUBED, tap the .375 bullets thru gently, slowly... Might, MIGHT not break the die...
As said with all the cast bullets and gas check available or paper patch a .358...
Your bucks, Your plan, your time.... ENJOY. Luck.