Since the gun is .30-06, it should be just a barrel change since the bolt face is the same for all three cartridges, and the overall length should be OK for the magazine.
Things may have changed, but I don't think Remington will sell barrels, but will install new barrels at reasonable cost. I suggest contacting them as your first step.
If you want another brand barrel, as far as I know there are no prethreaded or partially chambered barrels for that gun, so you are looking at having to start with a generic barrel blank and turn it to the proper outside dimensions, thread it, and chamber it, headspacing as you chamber. That is a fairly complex and costly operation. I suggest contacting a local gunsmith and getting an estimate. I rather think the "sticker shock" might make the idea of living with the current caliber or just trading on a new gun more attractive.
Jim