Twighlight
Quantum Scribe
There actually is research ongoing, especially by Julian Barbour, along the exact lines that you're looking at. It's based on Mach’s Principle.
The problem with Mach's Principle is that ( like time ) things aren't quite as they seem.
We tend to imagine that what we see through telescopes is a whole universe 'out there'. But that is an illusion.....similar to the way in which the act of 'seeing' is presented to us as an active reaching out rather than a passive receiving of photons.
So it is with telescopes. The light from some far distant galaxy may have originated 10 billion light years away.....but the actual photon is here and now. We are not seeing 'the galaxy'...we are seeing photons from the galaxy. The moment we call 'now' is actually composed of bilions of different interactions that all had their origins at different times in the past......yet they come together in an illusory perception that we call 'the current moment'.
There is fundamentally no difference between a photon ( or graviton, which also travels at the speed of light ) from the far edge of the universe, and one from the star system next door, and those from nearby would have far greater energy that would outweigh Mach's notion of a collective force from all the distant objects. Nearby massive objects like the center of our galaxy would surely add to any such force and distort it......with the result being that inertial mass would be different in different directions, which is at variance with observation.
I would have thought that the very fact that inertial mass is not directional would indicate that it is not the result of some external force. Even the microwave background radiation has tiny variations that would indicate that Mach's distant force should vary..yet it doesn't.