Sell your Savage and buy a Remington 700 or clone? That's one way to get it done but it's not a Savage action. You still have to have a "smith" set up the shoulder and headspace. That takes time and $$.
Not as easy as swapping barrels on a Savage.
High mounts and rings so the barrel nut wrench will clear? You bet!
One piece Bench Source mount and high rings. The mount "fits" the action and doesn't hang over either end. And "all" the holes line up and and the base doesn't cover any of the action opening. No "one size fits all" bases for me.

Rear action wrench? That's another way to go.
If you don't use an action wrench, sooner or later u will end up with a very expensive paper weight?
Not as expensive as a Remington 700 or clone.

Not counting the cost of having the barrels set up by a smith and not taking into consideration the wait time to get the work done. In that case, you better plan ahead.

Like I said before, it works for me.
If you have any reservation about using an action wrench or not, get one and be done with it.
Mine is still in the box. Won't use it again. Swapping barrels without it and doing just fine thank you! ;D
If it takes two men and a boy to brake the barrel nut loose, IMHO it's too damn tight!
NEVER had one of my barrels come loose the way I do it and I also take pretty good care of them so they don't get beat up. And like I said before, it's a good think we all don't think the same.
As far as Jim Briggs (Northlander)? I'll leave him out of this. He's a good man. 8)