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The same applies to the Jewish position regarding Christian denominations - either Judaism is totally correct, or only one Christian denomination is.

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No necessarily. They can have versions that are closer to or further away from the truth. I don't see the logic of having one completely accurate religion:

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What isn't logical, is for their to be no true church that is entirely correct, because otherwise God doesn't care whether His message is intrepreted correctly or not

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Given the vast number of different religions in the world, and the fact Catholics only comprise 1/5 of the world's people, it would indeed seem that God doesn't care if his message is interpreted correctly.

We have already established that Catholics have no credibility with regard to interpretation of scripture (history clearly shows this). So God hasn't chosen to inspire Catholics to get the correct message. If not them, then who?

And the final point is, if God wanted to communicate his message accurately, he would have made sure that a clear, inerrant bible was written without clear contradictions. A lot of human suffering would have been avoided, that's for sure. And maybe less people would have gone to hell.