But even then, I wouldn't say "this is a true moral dilemma" so much as "the moral system is self-contradictory".

So, Kant for example thought that such moral conflicts were impossible, and he would have agreed with you that no moral theory can be both true, and allow for moral conflicts. But it's not obvious to me that the inference from 'allows for moral conflict' to 'is a false moral theory' is valid. I don't have some axe to grind here, I was just curious if anyone had an argument defending that move (or attacking it for that matter).