I will try to make this clear and precise, I hope I can do that
since the swing arc bottoms out below your left arm pit, if you allow your head to move forward, the left arm pit moves forward and with it the bottom of your swing arc moves forward. Clear?
ok
now we want to swing from the inside, to square which is impact, and then back to the inside on our swing path. well the square part of the swing is right about the bottom of the swing arc, are you still following me?

if we move our head forward we have now moved our swing arc forward so we should be striking the ball fefore the bottom of our swing arc and before the square part of our swing, so that will be an inside out angle of attack with an open club face and lead to push shots

now you are keepng your head behind the ball and therefore you are moving the ball more forward in relation to the bottom of your swing arc so your point of contact shoulde be on a squarer path with a squarer club face. which should produce a straighter shot and get you closer to drawing rather then pshing.

Now because our subconscious mind adjusts for many things when we move our head forward we may come over the top to get a square clubface, but our path will be outside in, which will produce shots off to the right.

what you describe makes perfect sense to me, hopefully what I ahve typed made sense to you