Hiding in the woods for 30 minutes is pretty much the only effective way to fight a missile heavy army of the same speed or faster. That or you could try my mongol strategy.
Against the Mongols, I ususally like to have a massive amount of Trebizond Archers(more than one stack) and I just rotate them out when they run out of ammo so I have about 30 minutes of sustained missile fire.
However, in that situation. Hide in a forest. Um... And survive, their spearmen won't be a huge problem, its going to be the UMs since they don't get screwed in forests. I'd set up the spearmen to be fodder. Then I'd use the BI and Trebizonds to flank.
If you can kill the King or capture him, it won't be nearly as tough since all his guys are low moral units.
The Skezlys will be one of oyur most valuable units. They are worth exponentially more than Turcomans. Put them really far out and have them harass the enemy(turcomans are a good target). Make them chase your horse archers and then use your HA to charge theirs and rout them because your's are better..
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