Time for the poor Khergit's to stop taking a backwords slide late game and fix their ever present seige problems which the Mongols even lightly armored as they were was still known for their seige abilities. Here's a base template I hope you will consider, and I even took the time to explain everything out to you and everyone else that wishes to read and added a bit of extra info in case you want to change some names around for the lords on the Khanate.
Peasants:
• Tribesmen
o Clansmen
Nokud
• Lancer
o Darga
Noyan
• Orlok
• Boyan
• Horse Archer
o Vet Horse Archer
Master Horse Archer
• Keshik
• Mangudai
Nobles:
• Tribal Chieftain
o Tarkhan
Ilkhan
Khesig:
• Bahadur
• Khesig Keshik
o Khorchin
Torghut
• Khesig Mangudai
o Khevtuul
Build options here without breaking the common Khergit/Mongol idea you could use: Bows, Spears/Lances/Polearms, Axes, Shields, Curved Swords, Throw weapons, and the Khesig carried maces. You also have Hunters, Steppe Horses, Coursers to mix around. Mongol units were no stranger to siege warfare. Without breaking the game I suggest The Khesig wear only the best Khergit armor, but have great weapons and bigger shields so they can get up close. Be glass cannons of a sort for siege warfare. The Khesig had warriors already proven on the field of battle and as guards now should be equipped more for close combat and less about maneuverability as they were the ring of steel around the Khan and not trying to outflank opponents anymore. Perhaps now you can even work in a good Spear and Shield build.
Reasons for terms used:
Nokud - A military title for the free warrior-retainers of the Mongols. These are the standard soldiers which make up the Mongol Army.
Darga - Commander of their unit and those with that have shown to have the best skill in their Arban (10 man squad) or Jagun (100 man squad/10 Arbans)
Noyan - Commander of their unit and those with that have shown to have the best skill in their Mingghan (1000 man squad/10 Jaguns) or Tumen (10,000 man squad/10 Mingghans)
Boyan - The general of a Khan, in command of a Hordu (2-5 Tumens), but not related by blood to the Khan.
Orlok - The general of a Khan, in command of a Hordu containing three or more Tumens. This title was generally applied to royal princes related by blood to the Khan.
Ilkhan - This title refers to a provincial Khan who rules as a subordinate to an overall Khan.
Khesig - The Imperial Guard and protectors of the Khagan.
Bahadur - The Mongolian nobility, they were generally organized into elite units of the Imperial Guard, rather than directly into the army and acted as the equivalent to knights.
Khorchin/torghuds - Handpicked Imperial Guard units tasked with following and protecting the Khagan and his wife during the day.
Khevtuul - The night guards, and the ones that were tasked with defending the Khagan in his yurt while out in the field. Night was the most dangerous as yurts had no solid walls and swords could penetrate the walls and hit the subjects inside.
Khatun/Khanum - This title is roughly equivalent to queen, and applies to the wife of a Khan.
Khan - While this originally appeared as the title for a tribal leader, it was later equated to king.
Khagan/Great Khan - Essentially translated as "Khan of Khans," equivalent to King of Kings, this title was reserved for the equivalent of the emperor of the Mongolian Empire.
Hope this helps!