Dave,
I don't understand how the dealer push has anything to do with a disputed hand. They are two unrelated topics.
Since you mentioned the "otherwise very good/fast dealer who regularly mucks all the cards and moves the button before awarding the pot." I'd like to question how good he really is.Speed alone does not make a good dealer. There is a proper order of functions that must be followed by the dealer. I will list what I teach all new dealers:
Kill losing hands (face down into the muck)
Push the pot to the winner
Move the dealer button
Hit the rake slide (for cash games if applicable)
Call for the blinds (and antes) while gathering all cards
Begin new shuffle
Good dealers may execute the above simultaneously, but unless you are moving the button to get it out of the way of the pot being pushed to the winner, disrupting the proper order of procedures will always cause confusion.
Dave, are you thinking the "dealer push" has something to do with pushing the pot?