But it just turns out that there's a limit in which the quantum world looks approximately classical.
But as a physicist I have no illusion that any of our theories are actually true. They are all models that help us making sense of an unimaginably complex universe.
0. Special Relativity is already baked into the Standard Model, which is a quantum theory. It's General Relativity that causes problems.
what about gravity? If we don't know the correct account of that, how can we know those are exactly correct?
So we really are stuck with quantum mechanics, and there must be a quantum theory of gravity. In fact, there are actually quantum theories of gravity (including String Theory), but we don't know whether they're the correct theory that describes our universe.
...unless I have understood it otherwise, but quantum mechanics is still an approximation of things we simply are unable to measure individually - mostly because of speed and have to resort to guessing that approximation of that limited time period, which is still too long. It would be the same as trying to guess position of a ship during voyage across the ocean and taking the smallest measurable time period as 100 years, in which the ship has been already sunk out of existence, while smaller time period would have given us better picture and quantum mechanics that we are able to use has exactly that issue - we are unable to measure and record particles at smaller time intervals. At best we can see trajectories of particles long gone.
Also, this book is not agreeing with your statement, to me which sounds like Religion(because you have no explanation at all!) and should not be part of Science.