I have tried to do my homework on this, but I am stumped, so I seek advice from fellow FTers.

I am looking for a reward ticket (using BA miles) on partner Alaska Airlines, travelling from SEA (Seattle) to LIH (on the island of Kauai) in June.

The Alaska website shows seat availability for every day in June, but the number of miles varies from day to day (either 20k, 27.5k, or 37.5k miles for each leg).

But when I call BAEC, they only show seat availability for the days that Alaska lists at 20k miles (and there are very few of those). (The BA website is useless; it shows no partner exists!)