I know what you are going through right now. We had the same experience when Filex collected donations for the flood victims in the Philippines. Luckily, we were able to get a big discount from one Filipino freight company.
Maybe you can ask discounts from freight companies whose main office is in Japan.
Or you can ask the help of Qatar Airways. Maybe with their flights to Japan they can bring those boxes in batches.
Or you can ask from the Japanese Embassy.
It was an experience that taught us that it is better to send monetary contributions than contributions in kind. The freight cost here will a big burden.