Here is what I use with my HW springers that have a "flat top barrel pivot block" and it works OK for me.
* Focus on a hanging string at 18 yards and loosening the top strap screws I use a tested torpedo level sitting on the barrel pivot block...
Ed,
What matters is the relationship of the scope to the muzzle. When leveling via the barrel pivot block, you are assuming that is it perfectly parallel ("square") with the barrel/muzzle. I would never assume that. Without knowing the tolerances or history of the barrelled action, you can't assume anything. Besides the normal manufacturing tolerances, the barrel may have even been subjected to any number of accidental or purposeful tweaks to compensate for internal-misalignment/pellet-drop/droop/etc.
Do you really think that your barrel is square with the receiver/pivot-block?
Using the scope-bore vector as your baseline will get you closer. As it does not depend on any of the extraneous gun geometry. And then verify it by shooting well inside your zero.
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