surely setting an assassin on a friend because their inactivity is affecting the war effort is about the most gamey thing I could do?
Is that friend's incompetence going to cost you the war? If so, would you kill a friend to win a war?
Sounds to me like an awesome opportunity for your character to do some soul-searching, and find out exactly what is most important to them: The friend or the war. Because, let's face it, your friend is hampering the war effort. Their inattention, incompetence, and negligence are seriously damaging the realm. Maybe they aren't the loyal, staunch friend you thought they were. Well, obviously they aren't, as they are neglecting their duty, and basically giving you the finger. So instead of steadfastly refusing to see what's happening, perhaps you should have your character re-evaluate the situation, and come to the realization that this "friend" isn't really what you thought they were.