I like to level the stock/chassis first, then mount the scope and make sure that is level/plumb (first using a plumb line, then later I check it at 100 yards with a leveled target), then finally, when I know the reticle is plumb, as the last step, I add my scope level (with the comfort of knowing it's right).
I do it in sort of an opposite way.
I have a smallrig plate used for videography that has a bunch of holes in it. It mounts to a tripod, and...
To this plate I mounted a pic rail. This very basic setup is what I use for all my scope leveling.
When I level a scope:
1) I put the scope in its designated mount (or a spare if necessary), but do not fully tighten the screws. I have it tight enough that there is a little friction, but light enough that I can rotate the scope within the mount.
2) I put the smallrig/pic rail setup on a tripod, and then put the scope/mount on the smallrig/pic rail and lightly tighten on the pic rail - enough that it doesn't move.
3) Mount a scope-mounted level to the scope and tighten just enough that it doesn't move on its own, but still can be moved.
4) Set up the plumb line and point the scope at it.
Now I'm ready to go through the leveling process.
5) Align the reticle against the plumb line by rotating the scope within its mount.
6) Once aligned, carefully tighten the scope mount screws enough that the scope won't rotate when you...
7) Rotate the scope-mounted level until it shows level, then tighten it per manufacturers direction.
You now have a level that is perfectly aligned against the reticle - AND - unless it gets dropped or something that screws it all up, IT WILL ALWAYS BE LEVEL TO THE RETICLE. This means that you can move it between mounts, etc. and never have to relevel it again.
Each time you want to mount it to a rifle, you:
1) Level your rifle in a vice.
2) Put the mount/scope onto the rifle.
3) Turn the scope in the mount until it's level shows the same as the level used for the rifle.
4) Carefully tighten the scope screws per manufacturer spec.
Very easy. Can't do this with rail mounted levels (which could also be off, depending on how the rail is mounted), and can't do this with stock mounted levels, which I think we've established earlier in this thread are two steps away from what really matters - aligning vs. the reticle.