I'm sorry you weren't able to find a cheaper price. You already now how hot & sticky it is in Japan in August, although I'm not sure how it compares with NY. Sounds like a case of leaving the frying pan to vacation in the fire to me .

Still, the CO tarrif you posted is a reasonable price - I've seen flights sell for much higher than this in August, Golden Week in May, and during Christmas/New Year time - so please don't feel too bad. (I usually have to buy air tickets at least 9 months in advance in order to visit Tokyo in May or New Year).

I hope your family enjoy their stay in NY. I'm certain you'll make it into a memorable experience for them.