You can also send a direct message on Twitter to @AlaskaAir with the BA booking ref and they can look up your Alaska booking ref, and can also swap out the frequent flyer ticket on the reservation.

You'll be able to upgrade the flight at the airport only if F isn't sold out, there's nobody else waiting on the upgrade list*, and only if you're willing to pay cash for the upgrade.

Neil

* I am assuming, of course, that the recently reported fiasco in the other thread is resolved