(Heh, I'm pretty sure being a college sophomore makes me an amateur too.)

Yep. Cox's theorem implies only finite additivity. Jaynes makes a big point of this in many places.

I'm not asking for an isomorphism in the reasoning of choosing a set of axioms. I'm asking for an isomorphism in the reasoning in using them.

For large classes (all?) of problems with discrete probability spaces, this is trivial -- just map a basis (in the topological sense) for the space onto mutually exclusive propositions. The combinatorics will be identical.