You should definitely try to book it on one PNR and just get one through ticket.

Be aware, of course, that BA 7072 is actually operated by Iberia, not BA, so you'll need to check in with them (not BA) when you get to BCN. You'll actually be on flight IB 4176. But Iberia should be able to check your bags through to RDU, or at least JFK. And of course, if you can stand by for the flight one hour earlier (BA 7070, really IB 4188) you'll have a better chance at Heathrow. Not sure how flexible Iberia is with that.

And definitely get it as one ticket RDU-BCN. I've checked, and aa.com will sell you that combination. Current price is $861 roundtrip (though I didn't try to minimize the cost outbound -- there may be something better) -- just make sure you select 'AA, Eagle and oneworld' given that there isn't an AA codeshare on any BCN-LHR flight.