Savage can be tough to find support for.
I put a Bell and Carlson on an old Flat Back and it worked well. Has the aluminum block. Not much of a long range style.
https://www.bellandcarlson.com/index.cfm?fuseaction=category.display&category_ID=1040
HS Precision has Savage stocks that can be be set up for long range.
Fits: Savage model 10 FCP / 12 LRP right hand short action detachable magazine with large tactical barrel contour.
shop.hsprecision.com
The lightest and most espensive is Pure Precision.
The Savage 110 Adjustable Altitude series stock is designed for the hunter or shooter that wants to save weight on their rifle but add adjustability without sacrificing strength and durability. Utilizing layers of carbon fiber, a lightweight super strong fill and weighing approximately 38...
pureprecision.com
Unfortunately McMillan and Manners have stopped making stocks for them. Although Manners may still do one for the SA Savage.
Another