Yes you can swap your barrel, and bolt head.
I would suggest a $12 dollar membership at savageshooters.com . There are tech articles complete with pictures that will guide you through the process. $12 well spent.
You don't say which way you want to go with the caliber . Up or down ?
I believe that the winchester short mag calibers are all built on large shank barrels ( not a problem ) vs standard shank barrels. If you get a membership to savageshooters there is a member / supporter that sells spec. barrels for savage from shielen and McGowen just look for northlander shooting supply.
Since your 270WSM has a bolt face of .535 any of the WSM's ( 7mmWSM , 300WSM) would work without changing the bolt face. Although changing it isn't that big of a deal.