Actually the six flights is the only way, How much did you get?

Try and book the BWI-JFK with Delta or AA (or any other airlines if available) and book the rest with emirates, check if there is any differance.

I once booked a flight to Tokyo when EK did not have flights straight to Tokyo, so I booked to Osaka and the Osaka to Tokyo flight was in Economy with JAL, but it was the exact same price as if I'm going to Osaka, as if the Osaka-Tokyo flight was free.