The solution is adding the "thrown" attribute to the mounted archer units. QWERTY discovered this fine workaround. The only negative is that the "missile attack icon" switches to a spear instead of a bow & arrow.

The list of units to search for and alter is:
barb chariot light briton
barb horse archers scythian
barb horse archers slave
barb noble horse archers scythian
barb scythian noblewomen scythian
east persian cavalry
east cataphract archer
east horse archer
east chariot archer
egyptian bedouin
egyptian chariot archer
egyptian general's bodyguard early
rebel amazon chariots
merc horse archers
merc bedouin archers