My first time inside Khan's Heart, a simple summary is: do the intrigues, raise infiltration by doing the easier challenges, and recruit agents to increase the strength of your network whenever possible. Forget about the activities which involve Khaganate coins for now.

I went in there blind: ties to the Bazaar, doing Subversion and poisoning. Wearing a Shadowy attire which lacks Respectable, so many Respectable challenges near impossible to do or locked out. Try to equip items that boost your Player of Chess attribute.

Doing stuff in Khan's Heart is quite straightforward, it's the preparation of the Cover Identity and Backstory etc in your Cabinet Noir which was a pain. High failure rate and each failure raises your Suspicion which brings you that bit closer to going to prison. Had to travel between Balmoral and Spite several times to lower Suspicion, lots of actions used.