This thing that keeps galaxies bound that we cannot see but can only observe the effects… I think the hunt for it will push us into new territory.
That being said, as you say there has been nothing yet found that violates GR/QFT.
If that's true we're hosed. There would be no insights, no way to theory ourselves out of it. Only nerds wailing futilely about dark matter on the internet. And sadness. And we wouldn't know it's because all our theories are correct, but we don't have the complete picture of the extra-Standard Model dark matter particles, or if it's because some variation of MOND is true, (although it's extremely unlikely to be a MOND variation) or if we're as wrong as epicycles vs curved fabric of spacetime.
Arbitrarily advanced is pretty strong in a world where some people think dyson sphere scale stuff could be real.
We wouldn't need a Copernicus to solve this problem, we would need a Copernicus, then a Kepler, (ellipses & non-uniform speed) then a Newton, (gravity causes ellipses and non-uniform speed) and then an Einstein. (gravity is warping of space-time)
If quantum field theory is as wrong as Ptolemy's geocentric model was, we're hopeless. Because QFT very well predicts the observations; our observations have no ellipses in them that invalidate circular orbits, our observations have no anomalous Mercury precession that invalidates Newtonian gravity, no speed of light being consistent in all directions to invalidate luminiferous aether. To say that we simply need a smarter theoretical physicist is simply wrong -- our current theories do not contradict the things we are able to observe.
We know that general relativity and quantum mechanics do not play nice at small scales and high local gravity. But we cannot observe this conflict. And that's nothing to go on.
We would need an observation which shows that general relativity or QFT is wrong about something before we could conceivably make foundational progress on making new or different theories. And every few months there's a new article about "Einstein is proven right again" or "LHC experiment shows all readings are nominal".