Recording picky artists...
Strange irony. Your 'problem' is the opposite of mine. So many musicians are used to recording themselves on their PCs that the art of recording an entire band together, live, is becoming a lost artform. I have trouble convincing young musicians that the best way to go is to get their act together in rehearsals, learn the music and play it together live.
Since the group you are recording is playing Turkish music, this is 100 times more the case than with a western rock or pop song. You SERIOUSLY need to consider casting away your 'one-track-at-a-time' technique of recording music. It is simply not suited to gettting the best performance you can get with artists from this school of music.
That's because the music you are recording is based on improvisation and microtone intervals. Not a rigid adherence to the western 12-note octave or other notions that impose artificial limitations on Asian music.
In a nutshell, the more comfortable you make these musicians feel as they are playing, the better interaction you will get between them... and the better improvisations and subtle adornments you will get with the micro-tonal intervals they are using. Live interaction with the other musicians is essential. You will destroy a LARGE part of what they do if you force them to work in such an artifical way (to them) as the PC overdub technique.... I can almost guarantee that you will lose a big part of the 'soul' of what they are doing if you break the group down and have each musican try to place their part in isolation (or listening to pre-recorded tracks via headphones) from each other.
I would suggest that you get the whole group together in a decent sounding room and try to record them all together as a band. Don't even try to make each individual track separate from the others. BLEED IS GOOD if you know what you are doing. Think in broad palletes of sound color... Even with an ensemble of 12, you can get a great recording with just one microphone placed in the right sweet spot. And it doesn't hurt you to have extra reinforcement microphones in strategic places while they are playing... that can give you some slack to alter overall sound when you mix.
Find the sweet spots for your microphones... even recording the entire room instead of individual instruments if you have the right microphones and pre-amps for the task.
It will be much faster with this kind of group -- and FAR MORE REWARDING AT THE END OF IT ALL -- if you let the group play multiple takes until they get a complete take they are happy with, rather than spending weeks getting together with each different musician, having them play the song over and over to a pre-recorded backing and then wondering at the end why it didn't quite work out.
The overdubbing technique is extremely limiting for soloists in Asian music... because they are trying to synch with something already done instead of letting their muse go with the live flow).
I know this from my own experience playing the rabab and sitar, as well as from recording classical Afghan and Hindustani groups. You simply have to let the musicians find the muse and ride with it... and your job is simply to capture the muse when it arrives.
If you have ribbons and figure 8 microphones, I would seriously considering a simple M-S stereo mic set up... otherwise, get the sound good in the room, find the sweet spot for your mics and CAPTURE, CAPTURE, CAPTURE until you get the take with the magic muse! Salam Aleikum!