Leap of faith we aren't doing philosophy or religion we are exchanging energy
I am going to stretch your thinking back from classic physics towards GR. Many of the concepts in GR does not require curved spacetime at all
https://en.wikipedia.org/wiki/Equivalence_principleEinstein combined (postulated) the equivalence principle with special relativity to predict that clocks run at different rates in a gravitational potential, and light rays bend in a gravitational field, even before he developed the concept of curved spacetime.
So what is the reason you need a curvature of spacetime, well to turn GR into a force that you see in classical physics.
In general relativity, objects in free-fall follow geodesics of spacetime, and what we perceive as the force of gravity is instead a result of our being unable to follow those geodesics of spacetime, because the mechanical resistance of matter prevents us from doing so.
See the simplicity here there is nothing special about matter here it just can't be moved out of the way. So Einstein defined an equivalence of energy replacing your force with spacetime curve. That equivalence links the curvature to energy in a very precise way or to be exact what Einstein says is that the curvature of space-time and Newtonian stress-energy are the same thing.
You are trying to not talk about classic forces, energy and avoid stress energy in your Bill Curvature statements and I am going like what the hell sort of theory is this!!!!!!!
Now it does get more challenging when we can't simplify to a nice reference frame like above but SR provides most of the answers which GR adopts.
To me you are sort of coming at this backwards you are trying to curve spacetime without first working out why you want to do that and specifically trying to avoid incorporating classic physics.
