I've got one - you could remove some weight, change the stock would be the most bang for the buck to start with. Already a 16" barrel, already needs a brake.
I have another custom rifle - in 308 also. It weighs 5 1/2 pounds with no scope, and has a brake. It is a wonder to carry and a beast to shoot! I am thinking of swapping it back to the 243 it was, before I "fixed" it. The recoil is stiff, worse than a 300WM twin it has, I usually grab the 300 instead, more capability on the other end, and no additional recoil.
Unless you are packing it up a hill all week, I'm thinking you may choose the do what I did with my Scout - NOTHING! It is good for what it is, and accept it at that. Every time I get in the Mule at the ranch with it, I am thinking, new barrel, new stock, new trigger??? And then I come to my senses, this is my truck gun, I can hit anything standing still inside 300 yards without dialing it, quit screwing with it, Mike! Sometimes, it takes not having something, to realize what you had.......