Perhaps we have different underlying philosophies in what it means to understand something. I feel like I understand something when I know the mechanism for it. And then I can abstract that mechanism, so that I understand other systems that rely on that same mechanism.

I don't disagree. That's why I put in this part:

The only way to have a terminating procedure to determine when you understand it is when you can predict your observations of it in a model that connects to your model for everything else.

That "connecting with the rest of your model" corresponds to what you might call "knowing the mechanism in such a way that it generalizes to other systems". For example, if your model uses the concept of a "floobel", then floobels must coherently and consistently fit in with explanations for other things.

So I agree that to understand something, you must not only be able to predict the observables, but do so using concepts that are common (causally connected) to the rest of the model and not just created ad-hoc for one specific problem. (If you could only do the former, that would certainly be a noteworthy success, but doesn't count as understanding. Rather, it's something like the guy in the Chinese room -- the person, of course, not the person+room+rulebook system!)

So I really overreached when I said:

Rubber is no more explained when you know it's "really" just molecular forces writ large, than when you merely knew how it works.

And I apologize for that, because it glosses over what was really the crucial point of contention. I would say that the involvement of molecules can count as having more explanatory powers, so long as your suppositions about "molecules" have implications beyond just rubber stretching. (Which they do in standard scientific usage.) What I meant by the statement above is that if you invent something called molecules just for rubber stretching, your understanding hasn't increased. The understanding happens when you identify the general mechanism behind both molecules and other phenomena, and identify how the rubber properties fall out as an implication.

So let's look back at gravity now: does our understanding of its mechanism generalize beyond just gravity? I say it does, though I could be corrected on this since I'm no expert on relativity. Our description of gravity's behavior relies on concepts like mass, the speed of light, and wave propagation, which are extensively used, with the same values, in contexts where gravity is insignificant or ignored. So it does involve more general concepts and mechanisms.

Perhaps what you mean is that gravity generalizes to a much narrower area than quantum mechanics, making it appear ad hoc relative to quantum mechanics?