The real problem is blocking with a shield slowing you down. Shielders aren't as good as in real life against archers because in warband if you want to block arrows, you'll never be able to catch the person shooting them at you.
In reality, whether holding a shield in front of you or holding a shield by your side, you'd still be able to run just as fast.
As a matter of fact, you'd actually be able to run FASTER holding a shield in front than by your side, because being unbalanced towards the front would force you to run faster to keep your balance, while holding a shield at your side causes you to be unbalanced to the left, and thus unable to run as fast.
In reality, the reason that shields require real effort to use, is the moment of impact.
In order to keep your balance when a force impacts against your shield, the shielder must push BACK with the equal amount of force, or risk being knocked over (Newton's third law). Without anything impacting against against your shield, holding it up is no different than holding a dumbbell in your hand and running with it - pretty easy.
So the best course of action is not to add unrealistic, gimmicky effects to archery, but to change the mechanics of shields.
-----
Now that we got that out of the way, my suggestion is this:
1. Buff shielders' movement speed when blocking to nearly full speed.
2. Significant movement speed decrease for a brief moment after blocking an attack. A good idea would be to make the speed decrease depend on the damage the attack would've done had it not been blocked.
OR for a more realistic but harder to implement idea:
Instead of a movement speed decrease, it would be an acceleration in the direction of the attack.
For example, if you're running directly towards an archer, and you block an incoming arrow from said archer, you would accelerate in the direction of the arrow shot (pointing behind you) and be slowed down.
However, if you're backing away from an archer, and you block an arrow from said archer, you would speed up while walking backwards (acceleration in the direction of attack).
The magnitude of acceleration would depend on the strength of the attack. This would apply for blocking both ranged and melee.