There is, therefore, no run-away gravity.
Or as per your original interchange of gravity <=> curvature there is no runaway curvature. You are actually on the same argument as Einstein.
Note here you have used the conservation of energy to formulate the constraint. I am not saying that is wrong or right just making you very aware of what your argument relies on. Always remember to outline what underpins your idea.
The idea also precludes energy going into the "structure of the curvature". If you imagine bending an everyday material some of the energy goes into heat, and atomic adjustment. This is the layman way of saying the stress energy tensor of space always disappears locally to zero AKA you can't build up energy in the structure of space itself. You are on good solid ground with that because of the detection of gravity waves which match Einsteins prediction. This is an example of how experimental results can rule things in and out.
Ok I am going to make a rare thing a statement, to see if we can get you to bring it all together into a field theory. So lets assume there is a field which is our curvature (again be clear we have a concept underpinning our idea). You have in the above got to the point the gravitational field's potential energy itself contributes to the gravitational field. So if we turn the curvature into a field you have now reached the point where you should be asking yourself can the energy of other fields create the curvature in spacetime?
As a start point we use a simple proton which is three quarks bound together. Those quarks have very little mass but when they bind together the mass of the proton is 80–100 times greater than the individual masses. So here we energy in a non gravitational field doing something interesting. The more detailed background is given in the section "Quarks and the mass of a proton" in here (
https://en.wikipedia.org/wiki/Proton). As discussed on the page QCD just so happens to give the right answer to what you measure experimentally as it will everywhere it has been tested.
Inbuilt into all that you now have a new interchange to get happy with "spacetime curvature" <=> "gravitational field". If you aren't happy with the interchange then you have a new problem you can't reconcile Gravity with Atomic theory and you will have to adapt or change one or both.
So you can reject the idea if you like but go and fix up the poor atomic theory and your world falling apart
I probably should also highlight a fact that got lost in all the GW150914 discussion is that wave of Einstein’s theory are those of a spin-two classical field. Remember there are multiple solutions to Einstein's theory and one can extend the standard model in certain ways. The detected wave is one of the few options that is compatible with both frameworks and sets the only valid value of a graviton mass to pretty much zero. It is covered losely in the section "Speed of gravitational waves and limit on possible mass of graviton" in here (
https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves) and no dispersion was observed and the max mass limit is very very low. It basically was last nail in coffin to theories like MOND but also the first step to joining QM and GR.
This is one of the big problems with science media communication, they don't consistently use the same terms. For a scientist the words "gravity","spacetime curvature" and "gravitational field" are interchangeable but that is not obvious to a layman.
