Is there actually any other FF programme where you can send your EK miles to? I know that you can redeem with a number of (mostly asian) airlines, including TAP and EasyJet in Europe and JetBlue in the US.

The "double dipping" of miles (for the flight and for purchasing the ticket) is possible with all credit card reward schemes, and I think you should buy the ticket using your preferred credit card.

Personally, I collect EK miles on EK flights, Miles & More points on all credit card purchases and will most likely redeem my EK miles with TAP (the cooperation comes in handy as Mrs. Bruce desperately wants to visit Lisbon).