We went the public route, but from friends I know that the following additional costs normally occur for private education. As your yearly estimate is quite high, maybe you took part or all of it into account already, so just in case:
Private from JHS:
- Juku from grade 3, 4 or latest 5 including extra courses in summer and winter
- Fees for each entry exam, it is not uncommon to take 4 to 8.
- A fee if you want to keep a place
- School Entrance fee
- Yearly donations (voluntary of course, but many feel obliged)
- Commuting fee
- In the Tokyo area, the training facilities for sports clubs are often far away from school, that adds to the commuting fee.
- Very expensive school uniforms and other mandatory items. (unlike in public schools, bags, shoes, shirts, sweaters, socks and etc. cannot be freely chosen)
- Sport uniforms in case of sports clubs
- Very expensive (overseas) school trips
- Juku for University for 2 - 3 years, and again the same principle applies with exam fees for many different universities, unless you child gets a place per recommendation. (Just asked our oldest, he said it was more than 200,000 Yen for 9 exams at 5 universities.
Another possibly costly factor although not related to education, are orthodontic treatments, as those are not covered by Japanese health insurance and can easily cost more than a million.
Last but not least, in case your children opt for ballet (may be ice skating too) as naraigoto you can expect very costly happyokais on a yearly or two yearly bases, also, but cheaper, if the play an instrument.
Good Luck