I changed my steering implementation to not always snap the sprite's orientation to the velocity vector. This was causing issues where slight bumps (asteroids, lasers) were making the agents freak out. Instead, now the sprite is on a separate game object that can turn independently from the 'engine', and always tries to face the player. It's a little unnatural to see a rigid vessel like a spaceship having decoupled movement and 'vision', but I rationalize it as the invaders have developed advanced thrust-vectoring engines that let them essentially hover and turn on a time.

Oh, I also changed the orientation to landscape, which gives me quite a lot more screen real estate, which was sorely needed.