Rebore involves drilling out the barrel and recutting riflng to the different diameter..you will have pretty much the same chamber dimensions (308,338,358 based on same)which will have to be cleaned up as well.

I don't think your going to have enough meat on the barrel to rebore it although reboring usually works really well. If you go replacment barrel the contour will probably be a little heavier and then you will have to open the stock a little bit . That might or might not affect the balance negatively. I would look for a lightweight 338 federal possibly a Ruger Hawkeye in 338 or 358 winchester, T3 lite in 338 Federal and or a Kimber 84M in 338 Federal