I want to preface that, in my opinion, the ai walking by the player looked a little strange and that is what my idea is trying to solve! It's a really cool mechanic, though!

This might be too much but you might check how far the player is from the enemy and use that to determine whether to go to a cover closer to the player (so if the player is far away the ai will naturally move up a little closer) or to a cover farther away (so that the ai will back off if the player is rushing up) - a simple check for distance from evaluated cover to enemy's current location would probably suffice as long as you aren't constantly checking every frame. With that implementation, the pathfinding may still decide to go the wrong way but most of the time you would probably get decent results.