I hunted Kyrgyzstan a couple of years ago. You can find my hunt report here:
Hunting Ibex in Kyrgyzstan
The company I hunted with was Tour Khan Tengri. Their web pg is here:
CONTACTS | Company
Another option is booking through Igor AKA Ibexhunter. He posts on several web sites. Africa Hunting.com and accurate reloading.com forums. He has a special most years that run $3800 or so. On the accurate reloading forum there is a recent hunt report from someone who hunted with Igor's company. Tour Khan Tengri has a new "director" [ CEO, Pres] so I don't know what they would be like for sure. Igor might be able to tell you. It is quite an adventure. Any questions feel free to message me. Bruce