When you clamp the level on the barrel, how do you make sure the action is level side to side, level across the bottom half of the bottom half of the scope rings?
usually, once the bases are attached, that's your spot to level out the gun.
To answer MW's question, I do both. I've mounted scopes since the mid-60's and back then and up to 2017 I used the shoulder method. Since then when mounting scopes for customers I use a Wheeler set of levels for mounting.
My uncle used the shoulder method of scope mounting. He had a lot more muscle to him than I did in the early 60's. I think I could have slipped between the slats on a fence back then. Anyways I picked up his deer rifle one time and the scope was really off. I realized that his shoulder pocket was different than mine because of the muscle.