There is another way.
I use an oak block lined bench vise on the barrel and nut wrench instead of an action wrench and nut wrench. With a properly milled (flat) recoil lug and antiseize, you only need a firm grip on the action to keep it registered while tightening the nut as it travels down the threaded barrel to the lug.
For me, it was easier to make a set of oak barrel blocks using a Silver and Deming drill bit and a press, but it's 6 of 1, half a dozen of the other. I do dust the oak block halves with rosin for a good grip on the barrel. Now with a Remington 700, an action wrench is a must due to the tightness of the barrel to receiver threads. With the Savages, you can spin the barrel into the receiver by hand if the threads are clean and lubed.
I see you fletch your own arrows. When I was heavy into Tournament Archery back in the 70s, a good shot went through a lot of nocks and fletches. I did my own also. I Even had a hot wire feather cutter. That was back in the days before the compound bow, to give you an idea of when long ago that was.
Hoot