They all have the same prices. The question is if the particular airline has availability on your travel dates in the lowest booking class, and certain days of the week might be ~$100 more expensive.

In Japan summer is September so if you leave after Sep 1 then the rock bottom price on UA is $1264. In August you will pay in the $1500s.

The weather starts to get nicer in the US in early September in Philly while it is still muggy summer in Japan. That's when I would go.

You could consider flying to EWR and then taking ground transport to the Philly area if you want avoid connecting in the US, which can be unpleasant. I would advise against connecting in IAD.

DEN might be a good option since they do not have much international traffic. There is NRT-DEN on UA and I think they generally don't have very full planes on that route. This could also be more comfortable if the plane is not very full, although I have heard that the config in economy on the UA 787 is not very nice. You will also avoid thunderstorm delays via DEN, which are common on the East coast in the summer.