I worked the system starting in London, too. Finnaire was too expensive, even with a Saturday stay, and AA requires Iberia tickets to be nearly full fare to earn credit. But virtually all British tickets count on AA. (I can't speak for counting on CP, though).

My solution: British roundtrip LHR/MAD, 240$US with a Saturday night stay (I can recommend a good cheap hotel in Madrid!). Iberia roundtrip to Bilbao, Valencia, or Seville are all about 230$US for full-fare coach. A morning flight from London arrives ~2:00pm, leaving plenty of time for the IB turnaround.

BTW: I would avoid Barcelona/Madrid (215$US roundtrip) on Iberia, because it's a "shuttle" flight and you don't get any sort of receipt to show you took the flight (see separate thread). 15$US extra for the other destinations is well worth it, IMHO.