OK I'm with you, to be honest I am not so keen on the job either, I was thinking thread milling them was the way to go, two tool changes+slit saw, it would mean more waste (for work holding) but the hex head would be nice n simple
I would see how far from the 12mm the sample was and speak to the customer if there was anything wild going on.
I am sure with a thread mill you could sneak your way in till you hit the sweet spot then run 12 off..... but Iv never cut Peek....

I get the feeling the issue is one of material over an uber precise M12