CAI used to be renowned for long-haul bargains with TK and others.

It is worth noting that Elite members - which you are once you pick up the single TK flight - earn a 160% bonus when flying TK metal in Business Class. These are also status miles. So you only need 9,375 actual flown miles in TK J to earn 15,000 status miles. That's a single return in J between IST and SE Asia or North America for example.