It's also about whether a pony whose rider was shooting at a target directly behind him would be able to outrun heavy cavalry who don't have that disadvantage. Admittedly, the heavy cav would be slowed by the weight of armour, however wouldn't the army give their bigger horses to the heavy cavalry? Just as eleven-times world champion Usain Bolt is tall at 1.95 metres, the longer legs of the bigger horses might enable them to run faster over a significant distance. Of course, in the game the horse archers will outrun heavy cavalry as long as they run (unless they are unlucky or very tired). Also, I know that the issue is more about control of your units - you want to be able to order horse archers to run forward and to shoot at a specific target (the unit pursuing them). That sounds like a reasonable criticism of the game to me.
You're right, my first option relies on the auto-fire targeting the heavy cavalry. If this happens on the flank of the main engagement, I wonder how long it takes for horse archers (pursued by cavalry) run far enough that they are beyond the range of any enemy but their pursuer? (Of course, this depends on the direction they run in). My thinking is that, even if the auto-fire targets another unit, you might just lose that one volley - and that volley will be targeted at an enemy unit (admittedly, it might cause 'friendly fire' if the other enemy unit is in melee with one of yours, as you said earlier.) For example, in a
tournament battle between Parthia and Rome, Maximus Decimus Meridius (playing Rome, and commenting in the video) pursues Noble Horse Archers with Legionary Cavalry at 3:20. About three seconds later, the Noble Horse Archers fire a volley at some Roman infantry, not their pursuers. However, if you watch the Noble Horse Archers carefully at 3:30, they fire at the cavalry pursing them.