Generally speaking, using major national road is the shortest route in Japan.
For example if you will start riding on route 3 from Fukuoka, route 2 from Shimonoseki and route 1from Osaka, that will be probably the shortest route from Fukuoka to Tokyo.
But unfortunately these major national roads are not suitable for cycling at all because of too many cars and trucks etc.
So I think it may be better for you to spend some days intensively for riding in a pecific area where you are interested in and to use a highway bus with your packed bike for passing through other uncomfortable area.
I hope you will enjoy touring in Japan.