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Is it not more probable that we have, once again, run up against the boundaries of our current understanding of how things work and need to improve our models, than it is that this incredibly convenient substance actually exists?

Well, I can only add this: The scientific method is sacrosanct and infallible. It is beyond anthropomorphic influence. Current observational evidence indicates that dark matter and dark energy exist.

Certainly something is strongly influencing the orbits of stars and other matter within galaxies. Also, something is bending light in areas where we can't detect anything via observation. For lack of a better term that might describe this entity, "dark matter" is used as a kind of placeholder. More knowledge will describe what we're observing.

Mathematical models are useful in guiding our explorations. There is no substitute for observation, however. As you've suggested, models must acquiesce to observations. This happens continuously in physics.

You seem to be saying that scientists are being misguided by the lure of dark matter and dark energy. Here again I invoke the scientific method as insurance that, no matter what dark matter and dark energy ultimately turn out to be, scientists will not be drawn away from the course of knowledge that reveals what is causing the gravitational anomalies we are seeing.