Well, if you were to credit those flights to BAEC, you'd be a Bronze member by the time you arrived back at LHR from TLV, and only 40 TPs off Silver by the end of the itinerary (which you could get by taking the cheapest AA F cabin flight you could find out of WAS).

If you flew BA again, Bronze would get you free seat selection 7 days from departure, Silver would get you it at time at booking - and far better seats as well because non-status members who didn't wish to pay would still be waiting. Silver would also give you US lounge access on AA domestics.

You might find the system works rather better for you at that point