Yes I playing Bizantium too and have also Jihad against capitol but greek fire;walls ; varangian guards and mortatois archers (I love them ) give me good advantage
I was beat all of them but Kwarhezm send against me 4 armies.Now I end 150 turns and Kwahrezm beat Turks Cumans;half of Mamluks and have ca 50 provinces.They are beat Mongols easily
Look at first 50 turns.Moors are leaders very often at the beginning and they are lost with power ,production and people to Kwahrezm at next turns.Kwahrezm not fighting with others nations just conquer a lot of sovereign cities.