Ten days is where a Naryn-region detour becomes realistic without crowding out everything else.
Build on the 7-day plan (Bishkek, transfer, Jeti-Oguz, Altyn Arashan, south shore) and add a 2-3 day Song-Kul or Tash-Rabat trip in the middle — both are genuinely worth the extra days if you have them, and neither fits comfortably into a 7-day trip alongside everything else. Alternatively, swap the Naryn detour for the 3-day Ala-Kul trek if trekking matters more to you than the yurt-and-lake experience.
Either version leaves a day or two of slack for weather, which the Tien Shan will occasionally ask for.
Zoomy