I think we should try keep numbers of axioms low. (aswel as try to find new ones, hehe )
I was thinking about these:
And also my distinction of thing that is creature. It would seem to me that these can be merged. The external world is just something with a specific nature, and creatures are just things too, only we attribute Consciousness to it. I do think it is restrictive, but interesting nonetheless.
When coming to philosophy of physics the external world thing probably has to return, since axioms like "uniformity of universe behavior" have to be defined.

I was also thinking about DChristopher's axiom about afterlife that i "refuted" and what hidden axioms was needed there. The sentence i mentioned: "but it is foolish to make decisions which are senseless with respect to the physical world, on the chance that one will be rewarded for such senselessness in an unseen, spiritual world." seemingly implicitly states the chance on such a thing low. But why? I am guessing we could argue this by making another axiom.
-The simpler explanation is more likely to be true.
I am not sure if this is logic from probability-theory(and associated axioms) or an axiom though. And if you want to reduce it to probability theory, you will have to deal with the interpretations of probability theory too.(which is a topic on itself)
Another way of refuting it is the "uniformness of nature" axiom, with which existence of an afterlife would (uhm perhaps)violate. Because people presumably do not die in afterlife, and because it is unclear how they arive it this afterlife.(hehe, repeating what DChristopher said, in a way)
Another axiom-idea that:
-axioms may not say anything about the external world
If you think it is reasonable to presume that the afterworld is a form of external world, and its existence would need an axiom, it would "refute" the irrelevant-afterlife-axiom too.

On my "ethics-axioms", i have the viewpoint that these are really goals, but you can base them on axioms.
About that, what you said here, was really meant with this sentence.
With the sentence DChristopher mentioned, I was aiming more on how to achieve increasing 'average feel good', in the face of not knowing what other people feel. (and as you noted, if you think people are not clever enough to use their freedom to be happier, do not give it to them)