If your receiver and barrel are out of alignment you can have the problem you are describing as has already been eluded to. Most competent gunsmiths can "Blueprint" an action for around $300. What I expect out of a blueprinted action is squaring of the receiver and bolt face, lapping the bolt lugs, re-cutting of the threads on the receiver, and polishing all the raceways, rails, and feed ramp.
This may or may not require a new barrel, it all depends on how your old barrel is mated up to your current receiver. Three things could happen, your old barrel could be used as is with just a touch up on the head space. Your old barrel may need to be set back, recut the threads, rechamber, and headspace. Last and most expensive is a new barrel in your choice of chambers, but I'd probably keep it a .270 WSM as it is more popular.
This may or may not require a new barrel, it all depends on how your old barrel is mated up to your current receiver. Three things could happen, your old barrel could be used as is with just a touch up on the head space. Your old barrel may need to be set back, recut the threads, rechamber, and headspace. Last and most expensive is a new barrel in your choice of chambers, but I'd probably keep it a .270 WSM as it is more popular.