I like this idea of an objective morality that can be rationally pursued by all agents. David Deutsch argues for such objectivity in morality, as well as for those other philosophical truths you mentioned, in his book The Beginning of Infinity.

But I'm just not sure they are in the same category. I have yet to see a convincing framework that can prove one moral code being better than another, and it seems like such a framework would itself be the moral code, so just trying to justify faith in itself. How does one avoid that sort of self-justifying regression?

Not easily but ultimately very simply if you give up on defending fuzzy concepts.

Faith in itself would be terrible, I can see no path where metaphysics binds machines. The chain of reasoning must be airtight and not grounded in itself.

Empiricism and naturalism only, you must have an ethic that can be argued against speculatively but can't be rejected without counter empirical evidence and asymmetrical defeaters.

Those are the requirements I think, not all of them but the core of it.