I do agree that the Surprise would be better with 12 pounders but from my research i have only found that its largest cannons were 9 lbs. When it was refitted by the British when they captured her in 1796, this was the Armament:
Armament: Upper Deck twenty-four 9-pound long guns, Quarterdeck eight 4-pound long guns and four 12-pound carronades, Forecastle two 4-pound long guns and two 12-pound carronades. Apparent actual armament: Upper Deck twenty-four 32-pound carronades, Quarterdeck eight 18-pound carronades, Forecastle two 6-pound long guns.