From Boston, I frequently take LH F through FRA. F is much nicer on LH than any of the other options. The F lounge and F terminal in FRA are spectacular. This routing adds a few hours to flight time and a couple of extra hours on the layover, but overall the timing is better. E.g. leave late Friday night and arrive early Sunday morning. Any other routes involves leaving Saturday morning, arriving late Sunday and then just sleeping in your hotel till Monday morning. Going through FRA gives you a whole extra day in Tokyo.

Second choice would be F in NH via IAD, JFK, or ORD.

Third choice would be UA F through ORD or IAD.

JAL might also be an option, but seats are hard to get.

I would avoid business class entirely. It's much more comfortable than Y, but really nothing special.