Alexey, what about Mangudai and Tarkhan from AoE2? Maybe put them in place of some of the less well-known cavalry units?
It's better to replace Kok-Tengri himself with an emissary of Kok-Tengri, because there can't be several gods. It's better to lower the magic immunity to level 3.
The name of the capital – Karakorum – is perfect.