This page has the award requirements for AA partners, including TK. I'm not exactly sure how the AA codeshare works with award miles - but if like AA, that gives you two options.

I do believe someone posted about using TK within the last few months, but my brain Teflon isn't it letting it come through. They have A340s with two class service, and iirc it's not bad. TK2 / AA6000, 10 hrs from JFK, TK6 / AA6002 10:45 from ORD.

TK also has a nonstop to IST from MAN; perhaps AA has a seat to MAN, and you could connect?

Just take out that old nazar boncuk out while you call and keep it close.