If a friendly model joins the Monster in an attack, and the Monster barges the enemy away, then both the friendly model and the Monster are free to move to the next attack, just as in an Heroic Combat. Correct?

No, because of the second paragraph of this rule in the rule book (p.64). There is written that THE MONSTER moves again. Nowhere is mentioned that the other mins are allowed to do the same.

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Badner is right, I would suggest you to strike your friendly model attacks 1st then the monster as im afraid barge will throw the model off the friendly unit in base contact...

Attack with the secondary model first, unless you are relying on the monster to move further. Because if the first model kills the enemy unit then the model is unable to barge. (Correct me if I'm wrong on that)