Suppose the "simple" solution doesn't have the problems you mention. Somehow we get our hands on a human that doesn't have security holes and can't go insane. I still don't think it works.
Let's say you are trying to do some probabilistic reasoning about the mathematical object "foobar" and the definition of it you're given is "foobar is what X would say about 'foobar' after being exposed to every possible argument concerning 'foobar'", where X is an algorithmic description of yourself. Well, as soon as you realize that X is actually a simulation of you, you can conclude that you can say anything about 'foobar' and be right. So why bother doing any more probabilistic reasoning? Just say anything, or nothing. What kind of probabilistic reasoning can do you beyond that, even if you wanted to?
I think you're collapsing some levels here, but it's making my head hurt to think about it, having the definition-deriver and the subject be the same person.
Making this concrete: let 'foobar' refer to the set {1, 2, 3} in a shared language used by us and our subject, Alice. Alice would agree that it is true that "foobar = what X would say about 'foobar' after being exposed to every possible argument concerning 'foobar'" where X is some algorithmic description of Alice. She would say something like "foobar = {1, 2, 3}, X would say {1, 2, 3}, ...
What do I mean by "morality isn't logical"? I mean in the same sense that mathematics is logical but literary criticism isn't: the "reasoning" we use to think about morality doesn't resemble logical reasoning. All systems of logic, that I'm aware of, have a concept of proof and a method of verifying with high degree of certainty whether an argument constitutes a proof. As long as the logic is consistent (and we have good reason to think that many of them are), once we verify a proof we can accept its conclusion without worrying that there may be another proof that makes the opposite conclusion. With morality though, we have no such method, and people all the time make moral arguments that can be reversed or called into question by other moral arguments. (Edit: For an example of this, see these posts.)
Without being a system of logic, moral philosophical reasoning likely (or at least plausibly) doesn't have any of the nice properties that a well-constructed system of logic would have, for example, consistency, validity, soundness, or even the more basic property that considering arguments in a different order, or in a different mood, won't cause a person to accept an entirely different set of conclusions. For all we know, somebody trying to reason about a moral concept like "fairness" may just be taking a random walk as they move from one conclusion to another based on moral arguments they encounter or think up.
In a recent post, Eliezer said "morality is logic", by which he seems to mean... well, I'm still not exactly sure what, but one interpretation is that a person's cognition about morality can be described as an algorithm, and that algorithm can be studied using logical reasoning. (Which of course is true, but in that sense both math and literary criticism as well as every other subject of human study would be logic.) In any case, I don't think Eliezer is explicitly claiming that an algorithm-for-thinking-about-morality constitutes an algorithm-for-doing-logic, but I worry that the characterization of "morality is logic" may cause some connotations of "logic" to be inappropriately sneaked into "morality". For example Eliezer seems to (at least at one point) assume that considering moral arguments in a different order won't cause a human to accept an entirely different set of conclusions, and maybe this is why. To fight this potential sneaking of connotations, I suggest that when you see the phrase "morality is logic", remind yourself that morality isn't logical.