Note: “He [Hamilton] had stated the principles of it [the paper you cited, which was communicated to Madison by Hamilton] during the course of the deliberations.”
Hamilton was gone for most of the Convention. He left on June 30th. Returned for one day in August (13th) and returned for the remainder of the Convention on September 7th. There is no record of him presenting any separate plan other than the June 18th one.
His return on September 7th was after the September 4th draft constitution with the natural born citizen requirement.