They aren't "utterly incompatible", they're largely compatible. For example, lasers work here on Earth, and between the Earth and its moon. Moreover, hydrogen maser clocks and cesium et al.'s hyperfine transitions are used in clocks which are sensitive to nearby mass concentrations, and altitude above the Earth.

There are whole textbooks written on the limit in which General Relativity and Quantum Mechanics work well together, with Birrell & Davies 1984 https://books.google.co.uk/books?id=SEnaUnrqzrUC being the most widely used by graduate students (and as a reference book for researchers).

Indeed, such textbooks go into where GR & QM make incompatible predictions, and almost all of those are in the limit of strong gravity, which in turn is almost certainly always deep within an event horizon, or isolated in the very very very early universe.

Semi-classical gravity (SCG) works well as an "effective field theory", and simply marries a classical curved spacetime (General-Relativity style) with a relativistic quantum field theory (standard-model-of-particle-physics style). In particular, with minor caveats, on the cusp of strong gravity SCG is successful enough in the astrophysical study of stellar remnants that it is reasonably believed to be good everywhere outside black hole horizons and after the very early universe. https://en.wikipedia.org/wiki/Semiclassical_gravity -- one of the caveats is noted there, namely given a sizeable mass (> kilograms) brought into a superposition of space, it is not clear at all what SCG predicts a cavendish apparatus or other gravimeter will point to. This is a possible incompatibility of SCG's two more-fundamental theories in the weak gravitational field, low-energy matter, and low-speeds-compared-to-c limit, and is a puzzle that hopefully will be informed by clear experimental data some day.

Since we can't get information back from inside a black hole horizon; can't see anything in the very very early universe (electromagnetism hadn't "frozen out" of the GUT yet for instance); direct detectors of very early universe gravitational radiation are implausibly hard engineering tasks; and a bowling ball sized mass will be extremely hard to keep in a coherent state for reasonably long periods of time; these are really academic problems rather than practical ones.