I have confirmed the following flights are available; you may want to play around with some dates and try na stopover in London one one or both legs:

Flight 1: John F Kennedy (New York) to Istanbul

Flight Number: BA114 (New York to London)
Cabin: Club
Departure: Tue 12 July 2005, 20:30
Arrival: Wed 13 July 2005, 08:35

Flight Number: BA676 (London to Istanbul)
Cabin: Club
Departure: Wed 13 July 2005, 09:55
Arrival: Wed 13 July 2005, 15:40

Inbound Details

Flight 2: Istanbul to John F Kennedy (New York)

Flight Number: BA677 (Istanbul to London)
Cabin: Club
Departure: Wed 20 July 2005, 17:10
Arrival: Wed 20 July 2005, 19:10

Flight Number: BA117 (London to New York)
Cabin: Club
Departure: Thu 21 July 2005, 08:55
Arrival: Thu 21 July 2005, 11:15
Mileage and Fare Quote Details
Passengers BA Miles Fare Tax* Price Per Passenger
Adult 32500 £ 667.00 £ 113.20 £ 780.20
Total 32500 £ 667.00 £ 113.20 £ 780.20


GBP780 is about $1420 as quoted above.
You would need an overnight stay (v cheap on priceline about $60/night) for this to work.