I'm going to assume that you all don't know anything about Hamilton (listen to it, it's a great musical!), so I'm going to detail why certain characters from SM should fit with Hamilton characters.
P.S. I left a lot of in-jokes to the Hamilfandom and references to the musical itself. If you're a Hamilfan, see if you can catch them all!
Usagi as Alexander Hamilton (Main character, obviously.)
Rei as Aaron Burr, Sir. (Has a temper, is ambitious, and is probably the most likely to shoot the main character, and end up regretting it)
Minako as John Laurens in the place to be (both are close to the MC, and are pretty flamboyant)
Ami as Everyone's Favorite Fighting Frenchman, Lafayette! (Both have practical and tactical brilliance. Seemed like a good fit)
Makato as (that's right) HERCULES MULLIGAN!! (Both are one of the strongest and largest of the group, but are soft on the inside)
Mamoru as Eliza Schuyler (Romantic partner of MC. Done.)
Chibi-Usa as Philip Hamilton (Child of the MC and Romantic Partner. Done)
Michiru and Haruka as Jefferson and Madison respectively (Both are aloof jerks that soften up a bit by the end. Also, JeffMads)
Setsuna as Washington (Both are arguably the most mighty of the main characters, and take their jobs the most seriously)
I can't find anyone for the remaining Schuylers or the other minor named characters (like the Reynolds, Charles Lee, Eacker, or Seabury), so if you're able to help me with that, feel free!