You want to rechamber to "shoot more common ammo" in your rifle. Why? Lower cost? Availability? Selection? You can get all of that if you pick up a cheap Lee Loader and make your own ammo. Then, you wouldn't have any issues with the 1:14 twist rate, and would keep the collector value of the Savage. Of course, you could always sell it and buy a .223, if that's what you really want.
BTW, I own one. And I thought about rechambering it too, when ammo for it was becoming scarce. But after doing a little research, it just doesn't make sense to me. The .222 is a great varmint caliber with 40-50 gr bullets. And the .222/20ga combo makes a great "walking around" weapon. Can take birds, rabbits, fox, coyote, squirrels, and other small critters at just about any distance you're likely to see em. If you're looking to take anything bigger than that, you really need a heavier (longer) bullet. And, the 1:14 twist just won't stabilize much more than the typical 50-55 grainers.
If you really want one, Savage did make the 24 in .223. Might take a little while to find one, though.