Don't mod the chariots. They may be a major PITA now, but later, they are just a little nuissance. You can counter them with mass archers (fire arrows do wonders), or some heavier javelin infantry, like the velites or the auxilia after the Reforms. You can lay traps for them since they use a known patytern, they always try to flank you, usually from your left side. Position yourself where you have a forest on your left side, and hide some units in the forest (the Arcani lol). Conquer some more southern province and then hire mercenary Hoplites and watch those chariots getting crushed by your phalanxes. Try the wardogs. They are expendable and could keep the chariots busy long enough for you to dispatch the rest of the enemy army. Then you can proceed to kill them. I noticed that the chariots would not gladly charge on me if i have several Hoplite units. When i am dealing with an army that uses chariots, my phalanxes are always alert and on the move: i am constantly shifting them around to present their rows of pikes toward the chariots. Then they dont stand a chance. And i never ever allow my general to deal with chariots. His only purpose is to keep the morale high and to chase routed enemy units.
Tge AI never uses mass chariots (okok, the 'Amazons' do lol) so your 20-stack army is more than capable to deal with them

Y.