I suspect the next scientific revolution would be a refutation of Church-Turing

I'll give you long odds against. That would be tantamount to discovering a physical phenomenon that could not be described mathematically.

a bit like my understanding of the relation between Newtonian mechanics, and General Relativity and Quantum mechanics.

Those relationships are well understood: Newton is a low-order approximation of GR in the weak-field limit.

https://en.wikipedia.org/wiki/Post-Newtonian_expansion

The relationship between Newton and QM is explained, at least operationally if not philosophically, by decoherence:

https://en.wikipedia.org/wiki/Quantum_decoherence