While all of that is true, there are a couple problems. The first is managing to work AA plus two other OW carriers into the OW award itinerary without doing UK-US on BA (an AA rule). And, unfortunately the LHR-DCA return kind of leaves you up in the air, or more appropriately "on the ground", with regard to getting from the Middle East to LHR. If the OWE starts in the Middle East, then it must end in the Middle East - OWE rules:

FARES GOVERNED BY THIS RULE APPLY TO FIRST / BUSINESS / ECONOMY RTW TRAVEL VIA AA/AY/BA/CX/EI/IB/LA/QF/LP OPERATED SERVICES WORLDWIDE. TRAVEL MUST BEGIN AND END AT THE SAME POINT EXCEPT ORIGIN - DESTINATION SURFACE SEGMENTS PERMITTED AS FOLLOWS:
(A) WITHIN THE COUNTRY OF ORIGIN
(B) WITHIN THE MIDDLE EAST
(C) WITHIN SOUTH AMERICA
(D) BETWEEN THE UNITED STATES AND CANADA.
(E) BETWEEN HKG AND CHINA
(F) BETWEEN BANGLADESH AND BKK/SIN.
(G) BETWEEN MALAYSIA AND SIN
(H) WITHIN AFRICA

So the best that can be done here is a DCA-CAI roundtrip (11642 miles), or DCA-CAI,DXB-DCA (12873). For both a J OW award is 115K miles and an F award is 150K miles. For a J award you could fly DCA-CAI on AA and IB, and CAI-DCA on AA and BA. On an F award I would do DCA-CAI on AA and BA (on BA via YVR or YYZ), and DXB-DCA on CX F with the last leg from JFK to DCA on AE Y. Either way it is a minimum of 3 days of flying.

Now, if I am misinterpreting the rules then please let me know.