Where should I start in hosting international students?

So me and my wife have an extra two bedrooms in our house and like to have guests and wouldn't mind a bit of extra cash.

We have been doing a short-term stay domestic cultural program marketed as 町中留学(machinaka ryuugaku) 24-48 hour programs where we spend pretty much the whole time with the kids. While it almost fits the bill, it's really a little too much activity during that short time. And despite it being apparent that the kids' families or school are paying a significant amount of money, the compensation is very minimal.

So we're interested in hosting international students, high school or college making the most sense. I was wondering:

  1. What does it take to arrange an exchange for students at a local high school? I'm curious if it's as simple as getting an okay from the school and a little paperwork– exact flow of processes there would be helpful information.
  2. Are there any good organizations that take care of arranging this and aren't super greedy middle-men? (Yokohama if it matters)

by Different_Banana5186