Suppose I have a choice to make, and my moral intuition is throwing error codes. I have two axiomations of morality that are capable of examining the choice, but they give opposite answers.

If you're not sure which of two options is better, the only thing that will help is to think about it for a long time. (Note: if you "have two axiomatizations of morality", and they disagree, then at most one of them accurately describes what you were trying to get at when you attempted to axiomatize morality. To work out which one is wrong, you need to think about them for ages until you notice that one of them says something wrong.)

In a universe that contains a neurotypical human and clippy, and they're staring at eachother, is there an asymmetry?

Yes, the human is better. Why? Because the human cares about what is better. In contrast to clippy, who just cares about what is paperclippier.