I published my personal workaround when I goof around in vanilla. Links in signature.
One of the main culprits are the Mamluks. They're a 6700-man force, equal to the size of a large nation, hired for only 33 gold with a 2 gold/month maintenance cost. With Egypt's advanced technology and extra holdings, they're literally free mercenaries.
The Hashashin are also a secondary culprit, granting another 7k in cavalry and horse archers for some piety and no maintenance when in a holy war. So, they literally have ~14k FREE troops. My personal tweak is to have the Knights Hospitaller announced in 1099 (the date they formed) instead of 1113 (the date they're recognized), so the Muslims only have 9 years with the only holy order, rather than 23.
Finally, they have an already high retinue cap to begin with, which only increases. By the time the Crusades roll around, they've got 3-4k in cavalry on top of everything else.