Wirelessly posted (BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
The itinerary involving the lowest out-of-pocket expense would probably be:
SEA-ORD (10,000 Avios on AA/AS; no fuel surcharge)
ORD-DUB (20,000 Avios on EI; minimal fuel surcharge)
DUB-BCN on a low-cost carrier (cash price will vary)
The SEA-ORD and ORD-DUB legs would have to be booked as separate awards, in order to avoid BA's higher redemption rates for multiple-carrier awards; be sure to schedule a long layover (maybe even an overnight) at ORD to protect yourself in case of irregular operation of the SEA-ORD flight.