If worse comes to worst a badly pitted barrel with walls too thin to be reamed can be relined to a smaller gauge, such as a 20 gauge liner in a 12 gauge barrel.
The ready made barrel liners I've seen were a bit too expensive for my uses. Those were Browning made liners sold with top grade Trap or Skeet guns.
If an old double its likely the barrels are too thin to be reamed. I ran across an older Remington double that had been reamed far oversize and one barrel had split down the side.
Cutting the old thin barrels can pose another problem. Many such barrels are "Swamped" thicker at the muzzle than further back. When the thicker muzzle portion is cut away the thin barrel walls at the new muzzle can split under modern loads. That can happen with a barrel in otherwise good condition.