Writing a SciFi novel with gravity-manipulation. Would a physicist cringe or nod at this "mass as extra dimension" idea?

Dear Reddit-Physicists

Im writing a SciFi novel where gravity can be manipulated and I want to make sure this reads more like "hmmmm... interesting thought" rather than "magic in space"

I'd appreciate it if someone could tell me whether my “hypothesis” holds water or leaks like a sieve.

The idea goes as follows:
Mass isn't an inherent property of matter but a geometric effect: an object's extension into an additional dimension of spacetime. This dimension is imperceptible, like time: we don't experience time as a dimension but as change; similarly, we wouldn't experience this dimension as a dimension but as mass.

The single assumption:
This dimension is viscoelastic (it deforms under load semi-permanently).

A direct consequence of the core idea is that the equivalence principle (inertial mass = gravitational mass) would no longer be an “unexplained assumption” but a geometric tautology.

Concentrated mass has a disproportionately stronger effect than distributed mass.

Oscillating loads leave permanent deformations: standing waves that remain gravitationally active long after their source is gone.

At extreme density, the dimension stiffens. Further deformation costs disproportionately more energy.

Local deformation depends on the surrounding stress field. The density contrast matters, not absolute density.

What this could qualitatively explain:

Dwarf galaxies in voids behaving as if they had far more mass than visible matter suggests (strong expansion → thinned dimension → enormous density contrast from even small concentrations).

Neutron stars showing little excess mass (saturation + minimal local expansion).

Strain hardening implies a maximum possible mass for black holes; not from lack of available matter, but from the material properties of the dimension itself. GR doesn't predict this limit. If an empirical upper bound emerged that isn't explainable by environmental factors, this model would have predicted it; GR would be silent on it. 

I'd rather be told "this is nonsense" now than have a physics-literate read my novel, laughing at it and throwing it in the bin.

So long and thanks for all the input.
Andy