Theoretically this will work.

In the era past the scope of this game, say 17th or 16th century, cavalry was as big a menace as these Kataphractoi are being to you. I have an untested tactic against cav that takes from an earlier strategy for stopping a cav charge.

When the cavalry would charge, musketeers/arquebusiers would wait until the absolute last moment to fire their weapons, with the intent of killing the first row of cavalry, making a wall of dead horses and men to stop the charge of the cav unit.

In the game, I have seen arb and crossbow bolts hit horses and cause the unit, or at least major parts of it to stop moving, therefore losing their chargebonus. With arbalesters or crossbowmen on hold position and hold formation, one can take Fire at will off, and, with a good grip on timing and aim times, fire an ordered volley at the Kats at an incredibly close distance. Then, you will have only a few seconds to spare before the Kats start charging again, so in this time you should have units of your own cavalry or anti-cav attack infantry such as Halberdiers charge in and beat up the cavalry.

You will need to time the volley perfectly. This requires knowing whether the bolts are loaded or not, and when the group will fire. These things I have yet to learn.

You could also go get some Camel troops.