My suggestion would be to just get another gun. Why? Well, if you are talking about buying another barrel, then buying another stock, and then consider the labor involved (if you have a professional do it right - including glass bedding, pillar bedding, free floating, etc.) then the cost will almost force you to just buy another gun.
As for groups, don't worry. All Savages, for whatever reason, are shooters.
Also, if you get a heavier barrel, I also suggest getting it fluted, so that the heat can dissipate quicker.
Zachary