https://www.trapshooters.com/threads/robert-churchill-eyesight-and-the-master-eye.910472/Churchill clearly affirms "cross-firing", both transient ("dominance shifting") and "complete" (what we now call "cross dominance").
His cure is a properly fitting gun, focusing totally on the bird/target, and allowing "the eye" to determine forward allowance.
He does say "Provided that the gun fits...you will shoot exactly where you are looking and should kill every time. Misses occur from one cause-and one cause only-not looking at the proper place.
There is a confusing statement in Chapter V
"Your barrel must always be aligned precisely where your eye is looking. Apparently you are shooting straight at the bird but unconsciously your will be making all necessary allowances."
He is NOT saying to shoot directly at the bird/target but rather that "the eye" will determine where to look = the forward allowance.