You are fortunate with your .270. Most factory guns don't do that!

A Boyd's stock has made each gun shoot better than a tupperware stock for me.

You can switch to an accustock, and it is fun to build Savages, but a Boyds laminate stock will get you pretty much where you want to be quicker and with less cost.

Or, buy a nice one like McMillan, Bell and Carlson, etc. And you will be further ahead than the cost of the tooling to swap a savage into an accustock, unless you want to do that.