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PhilGoetz comments on The two meanings of mathematical terms - Less Wrong
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Relativity teaches us that "the earth goes around the sun" and "the sun goes around the earth, and the other planets move in complicated curves" are both right. So to say, "Those positions [calculated by epicycles] were right but they had it conceptualised all wrong," makes no sense.
Hence, when you say the epicycles are wrong, all you can mean that they are more complicated and harder to work with. This is a radical redefinition of the word wrong.
So, basically, I disagree completely with your conclusion. You can't say that a representation gives the right answers, but lies.
You're technically right about general relativity (so far as I grok it), but the hypothesis of geocentrism as understood pre-GR still fails hard compared to that of heliocentrism understood pre-GR.
Geocentrism doesn't logically imply that the earth doesn't rotate, but that hypothesis was never taken seriously except by heliocentrists, who then found experimental evidence of that rotation. Not to mention that epicycles were capable of explaining practically any regular pattern, and thus incapable of making the novel predictions of Newtonian gravity, which gives almost the right predictions assuming heliocentrism but gives nonsense assuming geocentrism.
It's far worse than just being more complicated; most epicycle-type hypotheses fail harder than neural networks once they leave their training set.