I have two options in mind to rebalance archers:
1)
Reduce the movement speed of archers by 50%.
The reasoning is to put an stop to prolonged, turn around, shoot, run, shoot. Or swiftly dodging cavalry couches. By allowing them that kind of movement speed you leave them without a counter.
A shielder is not a counter, because due to the shield he is likely to not catch up for a very long time. Hell I even have problems catching up with medium armor, no shield and 8 athletics.
2)
Decrease their dmg below a certain amount of meters by huge degree. At least 80%. I prefer this method, because it actually increase the usefulness of cavalry. It is simply idiotic to charge on the back of an archer just for him to realize it like 5m away turn around headshot your horse and demount you in a single blow, which is true for coursers and rounces and if he can aim for the legs a couple of the warhorses will be in severe danger aswell. I realize people hate the idea of buffing cavalry, but they actually dont have a role other then striking unaware people, bumping into dueling ones or attacking other lancers/1h cav - certainly not HA's. This is why I like idea 2 more, because it also stops an end to HA nonsense e.g. bumping a shielder and then shoot or running away from other cav for as long as it takes to get two shots out to drop the enemy horse.
However it also helps 2h guys to get the kill done, archers can still run and run and run, but at least they have to get to the threshold to do any reasonable amount of dmg.