Your challenge, should you choose to accept it, is to have a state known as the Republic of Hawaii exist no later than 1850 with a POD no earlier than 1700. Can you do it?
Do you want the state to survive? Because having Hawai'i republicanise just before its annexed by the USA is easy enough, but having it republicanise while remaining a sovereign state isn't so easy...
but having it republicanise while remaining a sovereign state isn't so easy...
There are a lot of republican sovereign states in the world. There were thirteen republican sovereign states that united to form the United States.
Yet no nation in the New World republicanised by Americans managed to remain sovereign (IIRC).
One might make the case for Cuba, even if it did later fall into revolution.
The Philippines, while not in the New World was republicanized by Americans and remains sovereign today.
The Philippines are sovereign today, but they didn't remain sovereign (through their history).