We have been communicating with Ms. Machiko Aso. There are two US carriers which go to Osaka, Northwest and United. Consequently, the trip on Northwest is slightly shorter. From New York, the fares are as follows from 1 June to 13 August. If paying by check, you will pay just the stated fare.
All dates above refer to the date of departure.
The fares quoted above are also valid for travel to Narita. From there, take the special express called Raicho to Toyama. You can only buy tickets in Japan for these trains. The schedule is not expected to change much for the Summer. As you know, apartments have been rented in Osawano.