kyrgyzstan - itinerary and best way to book yurts for Ala Kul Lake trek

Anyone do the Ala Kul Lake trek? I know it can be done in 3 days or 4 days but given my lack of time, I'm going for 3. If anyone has done it, please let me know, would love to have any advice. Here is the rest of my kyrgyzstan itinerary also. Any help is appreciated.

day 1 - arrive in Bishkek

day 2 - bishkek day trip to ala artscha (can i do this on my own?)

day 3 - Bishkek to son kul (8 hour drive)

day 4 - Son kul

day 5 - Son kul to kok kiya valley

day 6 - Kok kiya valley

day 7 - Kok kiya valley to issyk kul

day 8 - Issyk kul

day 9 - Issyk kul to karakol

day 10 - day 1 Ala Kul trek

day 11 - day 2 Ala Kul trek

day 12 - day 3 Ala Kul trek

day 13 - karakol to bishkek (though i read trek doesn't end in karakol actually so i need to figure this out)

day 14 - leave bishkek to tashkent