I've queued a rather long series of LW posts establishing what I consider the current state of affairs on FAI-related open problems, a few of which concern this issue (and of which the OP is the first).

Nice! Does that mean you have many new results queued for posting? What can I do to learn them sooner? :-)

Unfortunately, I also think that your non-self-referential alternative runs into similar issues (where subsequent agents use successively weaker axiom systems, if they follow the same general design).

Can you expand?