> If our unit of charge had been set when we knew about quarks, we would have chosen those as fundamental, and the charge of the electron would instead be -3.

Actually, I doubt it. Because of their color charge, quarks can never be found in an unbound state but instead in various kinds of hadrons. The ways that quarks combine cause all hadrons to end up with an integer charge, with the ⅔ and -⅓ charges on various quarks merely being ways to make them come out to resulting integer charges.