Having had no response after ages, I wrote back looking for a respose only to get this ill-thought-out nonsese:
Originally Posted by Turkish Airlines Finest
Please be informed BMI is no longer a member the Star Alliance so we can't evaluate positive your request, thank you for your understanding.
Therefore we are sorry that we are unable to meet your demand positively.
Kind Regards,
TURKISH AIRLINES INC.
CUSTOMER RELATIONS MANAGEMENT
It seems that they have missed that is precisely BECAUSE bmi is no longer in *A that I want a match.

I'll try one more time, but my past experience of TK is that once they have dug their heels in, they tend to stick to their guns, rather than lose face...