IE makes use of those words and means the same things as BE. But this introduces a vicious circle. If IE tries to determine whether "Eliezer should save person X" is true, he will notice that it's true if he thinks it's true, leading to Löb-style problems.

That doesn't seem like as much of a problem. We can posit that IE is right about ethics, in which case it would anyway be true that "Eliezer should save person X" is true if and only if he thinks it's true.