what if you could use 2 diferent suits for each action? That for example rabbit/fox to move, fox/mouse to battle, mouse/rabbit to recruit. This way you still have some randomness and noise, but its not as punishing
Another idea might be to add a 4th action that you can only take with bird cards. Similair to lizards sacrefice. Not sure what it could be but i leave that to you if you wanna do this idea