Balanced Units - A minimal balance mod for units

The nerf affects the Forest Archers more, but it also introduces more variety with 2 stacks instead of 1. The point of taking the enhanced arrow skill is that it also works in melee combat, so Forest Archers deal significantly more damage in melee than Armored Archers, and I think this breaks the game's logic.

I agree, but removing a skill that is the main "feature" of a creature is even worse, in my opinion. You could reduce their defense, and then the chances of surviving until melee combat become even lower than usual (and they aren't high to begin with).
Or, you should change the concept of the creature and, presumably, the entire line of Elven Archers. You could give the first tier damage (keep the double shot, + something else for damage, maybe even a direct arrow, and remove the stun), and give the second tier control (stun, knockback, increase initiative, remove direct shot and armor penetration). But this is already more than just minor changes.

Archers are not outsiders anyway, at least in 3.1, where Forest Archers were seriously nerfed.

They are.

Moreover, in terms of damage, 8-9 without a penalty is significantly better than double 5-8 with a penalty, both at long and close (melee) range.

That statement is unclear. At long range, 8-9 versus 5-8, at medium range, 8-9 versus 10-16. 8.5 versus 6.5 -- 13. It turns out to be quite balanced, except that in the first case, we have much more stable damage, which gives a tactical advantage. But the second one, combined with "Blessing," will be dominant, and we will lose a little at long range (-1/9 damage), and we will get the damage we need at medium range (almost twice as much damage).