+1. Unless you get the latest AA Business Class product, always go with BA or IB.

Keep in mind that some FT-ers do complain about connecting at LHR and prefer MAD. With BCN (on BA)now moved to depart from Terminal 3, the AA to BA connection (or vice versa) should be less painful.

The OP is free to spend his cash as he wishes and I admire the move to Oneworld as IMO they are usually the best, but as somebody who usually splurges on intercontinental Business, either with cash, miles, or buying miles to book J awards, I would never spend that kind of cash on a rather short and underwhelming Business Class flight. Particularly since we're talking about an OMA-ORD-JFK-MAD-BCN and vice versa within a week. Not much in terms of status can be earned from that.

On the other hand, it might just be possible to buy some LifeMiles with the current promo and book a LH or TK J award from ORD. Less money, better product...

Alternatively, just book a cheap Y itinerary without all the connections and pay for Main Cabin Extra in the three row mini cabin for "Premium Economy style legroom". Not great overnight, so I often take a daytime flight to LHR from ORD or JFK where I'm not worried about not sleeping and just sleep at a hotel near LHR. (you won't sleep much on a 7-hour JFK-LHR departing at 7pm anyhow)

Anyhow, just a different perspective...