Be aware that if you are willing to fly F in one direction, and J in the other, you could potentially save a lot of Avios on the roundtrip. Here's how:

BA offers a multi-carrier redemption option, in which the cost is based on the class of service of the longest flight flown (even if you were to fly in a higher class on one of the shorter legs). JFK-HND is slightly longer than JFK-NRT. If, for example, you were to fly JFK-NRT in F; HND-JFK in J; and then tack on a very short AA flight -- in any class of service -- from JFK/LGA on a later date (to give you the second BA partner needed to qualify for a multi-carrier redemption), you should be able to get the entire itinerary for just 180,000 Avios plus taxes/surcharges.

BA multi-carrier redemption table here:

https://www.britishairways.com/trave...e/public/en_us

Note that JL premium-cabin award space from TYO to the U.S. appears to be harder to find than premium-cabin award space from the U.S. to TYO.