What if the United Kingdoms of America had abandoned the Monarchy.
During the American Revolution many people revolted against the policies and taxes placed by UK for defence upkeep and it would devolve into a four year war before a peace was made where the colonies received de-facto independence from the UK while retaining the Monarchy, significant trade links and several treaties of mutual defence signed by singular kingdoms or groups of kingdoms(e.g the NewEnglish-British treaty, Virginian-British treaty, etc)
In the earlier parts of the revolution the idea of a Republic style government did appear when France, Spain and the Netherlands came out in support of the American colonies before the French dropped out in the 2nd year of the war due to the rather violent outbreak of their own French Revolution. This was a catalyst that caused Spain and the Netherlands to withdraw a significant amount of troops to defend its own border, leaving the Americans to fight alone.
While the combined power of these three nations may of emboldened to Americans to fully go independent as a Republic the main stepping stone is King George III himself. While George was never the most consistent or sane monarch he was rather swayed by the colonies plight and was a strong vocal supporter of the colonies.
His support was probably the main reason the various of American colonies retained the Monarchy and such close links to the UK afterwards and it was the unifying link of the monarch that made them united into the rather loose confederation that today is the United Kingdoms of America.
So what if the Americans did go fully independent and for Republicanism. How would this be achieved and what would be the consequences?