I never said overall group goal difference wouldn't apply, the only way it would become the first tie-break is if all 4 teams were tied on points as there is no need to do a head to head split in that instance as it isn't going to change anything.
If 3 teams were tied then the first way of...
If 3 teams are tied they would still go to the head to head results between those 3 teams first. You'd effectively be redoing the table expunging the results of the other team in the group as though they never took part. Only if all 4 teams were tied on points would the goal difference across...