It is difficult to do any detailed research with out knowing the approximate travel dates and the number of travelers.

I believe the only *A carriers with an F service TPAC are UA, NH, and OZ.

I did some award searches using the ANA tool and did find possible F availability JFK-ICN on OZ in early April, for two passengers. ANA lists the availability as "RQ" as opposed to "OK". This means there may be availability, but you would not know until you tried to book the award through your airline.

There doesn't seem to be any NH or UA availability in F.