Perhaps you might have more luck with the afternoon flights? (NH1011/NH1012)
EDIT: This commences as of 2013-08-31.
Looks like it'll be the old F product though, which may not be desirable.

I flew JFK-NRT on the afternoon flights (NH1009/NH1010) in F and the cabin was rather empty, but they were on off days (both midweek flights).