Be careful with cheap-o fares, at least on Iberia and Cathay. A friend discovered her trans-Atlantic flight to Madrid doesn't count!

In order to qualify for AAdvantage credit, the fare requirements are:
Iberia Y, M, and N always; D, L, & W transatlantic only; never on B
Cathay Y, B, H in coach; J, C, D, I in business
So Roti your LHR/MAD round trip may have to cost more.

My solution is to fly BA LHR/MAD r.t. (with a Saturday stay) since "all published fares" qualify. Then in Madrid I'll fly r.t. Barcelona on the Iberia shuttle - ~$200 r.t., in class YD (seems to count).

And since all your flights are returns, be sure to look at whichever second carrier you plan to earn the bonus on. For example, BA (my 2nd) needs Y or M on Iberia, the other fare bases don't count. But BA is more forgiving on Cathay.