Sorry for your loss....

Unfortunately... there are no CHEAP options.... even emergency/bereavement fares are still pretty expensive. However, they are cheaper then last minute full fare (maybe 10-20% less).

Here are some lower out of pocket costs I can think of:

Does your ANA friend have access to "buddy passes" (if ANA even offers that)?

Any chance at using UA miles?

Priceline?

I see IAD-NRT runs about 2400-3500 depending on your stay (actually I thought it would be more).