I agree, Looking at AS for JL availability is probably what i recommend as well. JL awards can be booked one way, if you see availability, id book it. Its not likely both inbound and outbound flights will be available so you might have to check again.
For tokyo, JL flies into NRT tokyo-Narita, and HND tokyo-haneda. For this search, you might indicate TYO for both airport search. Most people prefer HND however for proximity to the city.
Also note, KE also flies to Japan via Seoul. A caution for them is award space will book with roundtrip pricing. If only one-way is available, youd pay roundtrip award price for one way. Having both inbound and return available is a rarity unless you are ultra flexible. If you do find both segments, congrats.
Jiburi