I'm curious why some are removing the scope and taking it out of the action for a simple swap? I've never used a torque wrench either.
My scope is mounted really low so mine might be a little different than your situation. Heres how I do it.
1. Remove Scope (I have to do this remove the hand guard)
2. Remove the 6 screws on top of the hand guard clamp (The top piece of clamp has be removed or extremely loose for the hand gaurd to rock out.)
3. Loosen the back action screw slightly and loosen the front one about half way out. (If you don't want to take the action out of chassis or you can unscrew completely and remove chassis)
4. Tilt the action up slightly so the hand guard can clear the positioning screw then slide it off.
5. Then slide the barreled action in the barrel vise barrel first close to the action as possible to reduce as much flexing of barrel as possible
6. Insert action wrench (mines a surgeon wrench, the action wrench wont fit with my new scope on the action so thats another reason I had to remove the scope.)
7. Break barrel free
8. Thread new barrel in action then set in vise and repeat steps in reverse order.
Now, If you wanted to you could just slide whole gun in the barrel vise and clamp the vise down right in front of the hand guard without looseing or removing anything. But, If the barrel slips in the vise your going to have a nice ring where the vise destroyed the finish on the barrel(this has happened on both of my barrels but its under the hand guard and barely noticeable). Also hanging that much weight and torquing from that far down the barrel may induce stress(I really don't know for sure as I cant measure it give you scientific data but it looks it could).
I use a torque wrench for repeatability. I torque to 85ftlbs for repeatability, but Im going to try 50 ftlbs next time and see what happens.
Im not saying mine is the best nor even the right way and am open to any suggestions.