Ruger m77 mark1 needs a new barrel

Hey guys.

Ive got an old Ruger M77 in .270, I really like it the stocks shape and the action. BUT.. the barrel is pretty tired .its been shortened to 20 inches and the rifleing isnt the deepest.. in saying that its still relatively shiny and free from pitting but I think id like to put a new one on si can can get some half decent groups from it. So im seeing a few remington barrels around at the moment that people are trying to sell as the taken the actions for other projects and am wondering if they would be easily interchanged.. I want to have a bit of fun with this rifle and try my luck at a bedding job once ive sorced a barrel. But I dont want to spend much as its a trial project and the rifle owes me nothing as it was a hand me down. ..
Any feed back would be great cheers.
Tim