[Bozos of Bones]

Try using those Almohads' Militia, they're quite unkillable. Halberdiers are a cross between a swordsman and a spearman, not as good as either of them in their field, but versatile and mostly disciplined. They're great for defensive purposes(a group of halberdiers defending those catapults against enemy castle siege lifters). There's just one modification to your otherwise good strategy: have archers attack the fast and lightly armored, because even elite archers can't take down heavy armored cavalry(it's like killing a king with swordsmen, he will go down eventually, but not soon).