However, on neither TK not vayama can you mix CC and Y on the same ticket. I think I even had trouble trying to book JFK-IST-X, where no IST-X flights have a CC cabin. IIRC, neither Turkish nor vayama searches showed options with CC in JFK-IST.
Actually, it is possible on Vayama. I found this out unintentionally. About a month ago, I was trying to book a return Y fare JFK-IST-BJV July 11-16 and a Kayak search forwarded me to Vayama where I found a number of Y options and one that was Y from JFK-IST and Y+ from IST-JFK (Comfort, an A fare).
The ticket wasn't cheap (mid-July is the height of high season on that route) but the price difference between a regular roundtrip in Y and the Y/Y+ combo was negligible--like $20, not a bad deal for a 10hr flight in Comfort Class...and it really is much nicer than Y. Similar to domestic biz class seats on UA but with more leg room, nicer AVOD and much better food.
The other way to do it is at JFK. The TK desk there has seemed willing to do a 1-way upgrade to CC for 200 Euros when I've asked. CC never seems to be full.