Check on the alaskaair.com website and look for supersaver coach awards.

At best, using Avios you are able to book AS flights that are available as super saver coach -- looking at the AS website you can see for at least one of your dates that no super saver coach tickets are available (even to members of Mileage Plan trying to use AS miles).

. . . it matters whether Alaska is making seats available at the super saver coach level. If you look at alaskaair.com you will see that AS does not have any super saver seats available on March 15 SEA-SJD even for Alaska Mileage Plan members. It does not matter how many seats are sold/taken/available on the seat map.

And if you read that thread, you will see that only seats available at the "Super Saver" rate to Alaska members are also available to BA Avios redeemers.

And I'm not seeing anything available as "Super Saver" on your route in March - only at the higher "Choice" rates. That's why you can't redeem using Avios.

You're looking at the wrong type of ticket. You need to look at Alaska award tickets. There appear to be the following types:
Super Saver Award
Choice Award
Full Flex Award

Only when Alaska has availability for a Super Saver Award might there be availability shown to BA for you to book an award through BA.