I also doubt that initially the Monarchy would be that of an Emperor, but more of a King. The only two, possibly three, states that the Monarch would be directly titled king of would be Texas and Hawaii, where they could exist outside of the US yet still part of it - this gets around the question of the constitutionality of annexation. Alaska may be another one that can be shoed in a similar fashion. I always also consider California.
Before the Civil War, if a person from the USA said "my country" they could well mean their state rather than the United States. "Emperor" also fits well with the Roman-style pretensions of a country that established a Senate and adopted an eagle as its symbol.