Hi,
The problem is that it requires mouse movement as an additional input, and that is not allowed.
But I honestly think the idea of changing movement direction when pressing the fun button is not bad at all. In your post you say that it's not playable because the ship always shoots at the wrong time: I think that's 100% playable, it's just more difficult for the player, who has to time well when to switch direction to manage to shoot at the right position.
Think about it, I think you should end up with an interesting game ;)
-Cah