Coosa;
I am not a turkey hunter so have not entered into this portion of the discussion. I have killed a Grand Total of two turkeys in my life, both with a 12 Ga & a 1 3/8oz load of lead 4's. hey both did die Dead, on the spot, neither was extreme range by any means.
I did understand the purpose of your original post & it did very well illustrate the point of the fact the gun moves after pulling the trigger & before the shot exits the muzzle. The heavy shot load at a comparatively low muzzle velocity will give it just a bit more time to move, thus accentuating the problem, as of course will the very light weight gun.
I will also note the problem does also exist in an over/under as well. Their bbls also converge though not to the extent of a SxS. Due to the higher plane of its axis from the point of contact with the shoulder the upper bbl would have a tendency to center its pattern higher than the lower "AND NOT" just by the amount of separation of the bbls, which would be insignificant as far as pattern placement goes.