Okay, so I've decided that having Kina be a 17-year-old transfer student is better for character interaction and background, as her reason for transfer can be easily explained by backstory: Her grandfather died, so she has to move to a relative's home (probably an aunt or uncle) because she can't support herself in her grandfather's old home.
The home is just a "Quincy Dojo" now. It's just a training ground for Quincies, "publicly owned" by the Yoshimoto family.