No, we know that neither relativity nor quantum mechanics is correct, so the premise is already not fulfilled. And, as I said, too, it is very possible that we or mathematics fails to give a unified and correct description.
But I just read the part again and I probably misread it the first time. He is not talking about having absolutely correct but inconsistent or contradicting theories, but about theories that are correct, consistent and non-contradicting where we can test them and maybe even where we can ever expect to test them, but ultimately lead to inconsistencies or contradictions if we extrapolate them beyond experimental reach. This leaves us in a situation where the theories are in perfect agreement with reality but on purely theoretical grounds it seems impossible that they are correct. This is more similar to the situation of relativity and quantum mechanics but we have not yet reached the experimental limits and the theories are not even in perfect agreement with all available data. (I will read it a third time, I am still not totally convinced that I got it right.)
But I just read the part again and I probably misread it the first time. He is not talking about having absolutely correct but inconsistent or contradicting theories, but about theories that are correct, consistent and non-contradicting where we can test them and maybe even where we can ever expect to test them, but ultimately lead to inconsistencies or contradictions if we extrapolate them beyond experimental reach. This leaves us in a situation where the theories are in perfect agreement with reality but on purely theoretical grounds it seems impossible that they are correct. This is more similar to the situation of relativity and quantum mechanics but we have not yet reached the experimental limits and the theories are not even in perfect agreement with all available data. (I will read it a third time, I am still not totally convinced that I got it right.)