The convention did not approve the Randolph plan on the 19th - they rejected the New Jersey plan, resuming debate on the Virgina plan. Which still needed the 'Great Compromise' of the Convention to be acceptable to the smaller states.
But what insight! A win/win situation for you - Hamilton arguing for a plan that was adopted would mean he supported it. Hamilton arguing for a different plan means he really supported the other. Either way Hamilton wins, or does he? Hamilton chanced being forever remembered as a monarchist to force an acceptance of something less? Hamilton was the ONLY person advocating a monarchy:
Dr. JOHNSON. On a comparison of the two plans which had been proposed from Virginia and New Jersey, it appeared that the peculiarity which characterized the latter was its being calculated to preserve the individuality of the states. The plan from Virginia did not profess to destroy this individuality altogether, but was charged with such a tendency. One gentleman alone, (Col. Hamilton,) in his animadversions on the plan of New Jersey, boldly and decisively contended for an abolition of the state governments.Now who voted for what?
Elliot's Debates Vol. V, p. 220.HAMILTON: "Let one branch of the Legislature hold their places for life or at least during good behaviour. Let the Executive also be for life."
The Debates in the Federal Convention of 1787 reported by James Madison, 18 Jun 1787, Vol. I, p. 288.
Good thing you are not negoitiating with such a genius or you would be wondering where your pants went.
You might not be a genius, but I am - a member of Mensa. Touche.