Monaspa units
Monaspa was professional cavalry force in 12-13th centuries. These warriors were veterans of different nationalities and social classes. Mostly Georgian nobles who had lost lands and property, commoners who had proven their capabilities, Kypchaks who played important role in strengthening the Kingdom. Also Armenians, Kurds and others. For example, Zakaria Mkhargrdzeli, who was Kurd by nationality, became Amirspasalar(chief commander) of Georgia for his loyalty while serving in Monaspa.
Even though they were elite warriors, they weren't wealthy enough to get the best equipment. King was spending from state treasury for them. So, if we note that their number was a few thousand, then logically each of them couldn't have lamellar armor and only a few would have horse armor.
So, only Monaspa Guard should have horse armor and entirely lamellar/scale armors. The rest should have mix of chain mail and lamellar, also no horse armor.
All the Monaspa units should have elements of both Georgian and Kypchak(Cuman) armor to highlight their nationalities. There are some Georgian frescoes influenced by Kypchak/Rus equipment etc.
Let's sum up why they are inaccurate in Broken Crescent:
1)They have only scale armor.
2)They have Persian Pointed helmets which is completely inaccurate.
3)They have curved swords which belong to later centuries.
4)They have leather pteruges(roman leather stripes).
4)They are the best and heaviest units in the roster(Monaspa Guard should be one of the heaviest but that doesn't count).
Their Shields:
On Tier 1 they should have mostly tear shaped shields. On Tier 2 mostly round shields. Round shields should have metal reinforcements only in the middle and the edges. Same for tear shaped shields, mostly use painted crosses with some reinforcement.
@Khevsur has drawn these shields according to Georgian frescoes:
Round shields:
Their Helmets:
All Georgian units on all tiers should have only egg shaped helmets. Except Monaspa who should have Kypchak/Rus helmets as well.
Egg-shaped helmets:
Monaspa warrior with Kypchak equipment:
Rus helmets:
Their Armor
As i said, they should have both mail and lamellar armor. All of them should have mail coifs and chain mail on arms. On Tier 2 on legs as well.
Warriors who have lamellar armor shouldn't have leather stripes on shoulders and lower part of the body like in Broken Crescent. Instead they should have either chail mail or the same lamellar covers. Also many had metal spaulders.
Swords
They should have Byzantine type straight swords. Even on Tier 2, you should only partially use Georgian curved swords.(Georgian curved sword is noticeably less curved than others, just like in Broken Crescent).