One of the most common justifications for the consistency of large cardinals is the development of a coherent inner model theory for many large cardinal axioms. While the strength of this argument can be debated (has any axiom ever been shown to be inconsistent via the attempt to develop an inner model theory?), it appears to be pretty popular, e.g. it appears in Maddy's Believing the Axioms.
However, it is my understanding that assuming Woodin's HOD Conjecture, his Universality Theorem implies that given an extendible cardinal, there exists a weak extender model that reflects essentially all of the large cardinals that are currently studied.
If inner model theory can be extended so far in a single leap, can it still be used to justify the consistency of any particular large cardinal axiom stronger than a supercompact? If not, what is the replacement?
It's also my understanding that assuming the $\Omega$ Conjecture and a proper class of Woodin cardinals, the same class of large cardinal axioms can be ordered in consistency strength by the Borel degree of the initial segment of universally Baire sets $A$ for which they establish determinacy properties of $L(A, \mathbb{R})$. Would calibrating the place of a large cardinal axiom on this hierarchy replace other arguments for consistency?