We have a language of experience and a language about physical facts, and I don't see how using a word to describe both simultaneously does any work to actually bridge the two.

Wel, no, it doesn't bridge the gap because you can talk about pain in ways that you can't talk about c-fibers. Whether pain is spacio-temporal is a question you can reasonably ask, but whether c-fibers are isn't. The point is that nothing of value is lost if we stop talking about pain.

When your hypothetical person says "my c-fibers are firing" they are describing a state of physical affairs and presumably also their experience of what we call pain.

Yes, but why does this presumption pose a problem for materialism? Why can't he just be wrong about the fact that there is anything called "pain" which is left out of every possible description which doesn't involve Qualia. I can also reject the notion that there is something called a "meaning" apart from the physical state of affairs, and doing so makes his/her assertions even less mysterious.

and on the other hand the person can examine the facts about their own experience of pain

An intersubjective one? How? I can give an alternate account of "examining the experience of pain" which only assert the existence of brain-states, and if I wasn't familiar with concept of a "pain" nothing you have said would count as evidence against the fact that you are simply mistaken.

hen we hear that someone broke their leg, we are also understanding two separate things at once: they are experiencing physical pain, and there is a physical state of affairs that includes nerves firing around their broken bones, etc. We don't conclude that there isn't a gap between the two states of affairs.

Once again, why does people saying these things count as evidence (strong enough evidence to assume something as incredible as an "ontological realm") for something called "pain" when they themselves say that their physical constitution and therefore speech is totally unrelated to the matter at hand?