I have the action wrench, I've never tried to remove or install one without it. That being said, you MIGHT be able to remove and install one the way you're describing if you're willing to sacrifice the old barrel in the v blocks in the vise. You do have to have the barrel nut wrench, I can't see a way around using that. Savage barrel nuts are torqued VERY tight from the factory, forget 50-80, it's more like 200 ft lbs so you're going to have to have good V blocks or a barrel vise to hold the barrel tight enough to break the nut loose. Once the nut is loose you just unscrew the action by hand. You only need to put the nut back on at 50-80 lbs but they usually come torqued considerably more than that from the factory. When you install the new barrel and torque the barrel nut you're going to have to have some way of keeping the action from turning while you're tightening the nut. I'd imagine you can fashion some sort of piece of wood through the magazine cutout that would be enough to keep it from turning while you snug up the barrel nut.
I'll be blasted as a heretic for saying it but you don't even really headspace guages to set the headspace. I've installed several just using a piece of NEW brass. Do NOT use fireformed brass, only new. Use the new piece of brass as a go gauge and put a piece of scotch tape on the head for the no go gauge. Screw the barrel in with a piece of brass in the chamber until it stops. Tighten the nut and make sure the bolt will close on the brass. Put a piece of scotch tape on the head of the case and see if it closes, it shouldn't. If it isn't right then adjust it until it is. If you do want to use a gauge just get the go gauge and use the tape trick for the no go gauge.
For a belted case there isn't a fixed spec for shoulder dimensions so measuring the shoulder after firing isn't going to tell you much beyond how to set up your dies. The measurement that counts is the belt, that's why you only want to use a new piece of brass, a fired piece out of your old rifle isn't going to match your chamber so whether or not it chambers is meaningless with the new barrel. Different makers of brass will have wildly different dimnsions in the shoulder areas on belted cases. I've seen the shoulder grow as much as .017" on new brass shot in a properly headspaced chamber, the brass maker just made brass that was very undersized in the shoulder area.
