BA used to run 2 flights a day to Tokyo. This was cut to 1 last year. Tokyo suddenly went from being one of the easiest routes to get BA Miles seats to being one of the hardest.

However, trying to book this sort of thing 2 months in advance will always be difficult. There are 2 Finnair business class seats Helsinki to Narita on June 22nd, not sure if you can connect to these somehow.