Is it a pre-war sporting model Mauser? Weren't some of those built by FN? A pre-war sporting Mauser from the factory is quite collectable. Attach a photo.
Personally, if rebarrelled I would put another 30-06 barrel on it. The barrel on the late WWII Springfield my dad built for me was also kaput due to corrosion. I chose to put another good WWII barrel on it because 1) it was briefly my dad's gun before he finished building a second one and 2) that caliber is really hard to beat.
Also, are you sure the barrel is the problem? Is the barrel free floating? I strongly suspect not since that was pretty much unknown back then. Try to slide a piece of paper between the barrel and wood. It should move freely down to about 2" ahead of the receiver-barrel junction. If it's bedded to the end of the fore end (often the case for vintage sporterized rifles) use a round rasp to remove enough wood or glass to float the barrel. Then go back to the range. If it is already free floating, you might try adding a pressure point. Some rifles just don't like free floating. Loosen the action and slip a thick plastic tie down the muzzle to about an inch below the wood, retighten the action (tie should be stuck), and see if it will group that way. If it does, go on line to see how to add a permanent pressure point. Also, check to make sure the action is properly anchored to the stock. Is it even glass bedded? If not, that is almost certainly your problem. After I rebarrelled mine last year, I hurriedly rebedded the gun three days before flying out to hunt Africa. Got it zeroed before leaving but then it went wonky shooting at the first animal. Back at the range it was all over the paper. I switched to a loaner rifle from the lodge. Later I discovered the Springfield's bedding epoxy shrank as it cured and the action and barrel wiggled ever so slightly in the stock.
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