UA flies to PSC which is less than an hour drive from Walla Walla.

You could fly BHX-EWR-DEN-PSC entirely on UA metal. There's even saver availability for many upcoming dates.

Compared to interlining bags with a non-aligned carrier and spending extra $$ to transit SEA this seems like a no-brainer, even if you have to rent a car to go from PSC-ALW.