You know I'm not really qualified to answer but since you invited me, I shall try
Intuitive rubbish only of course....
...and the more I looked at your theory, the more I got to thinking this way.....
Could inertia be the result of your attempt to change the actual physical dimensions of the mass itself?
If you imagine an ACTUAL soap bubble at rest relative to you. If you push on it, just nudge it, the shape should change (flatten) and bounce back to spherical, if you continue to accelerate against it, I assume the shape remains the same (flattened) for the duration of the acceleration until the acceleration ceases, and then it becomes spherical once again due to the same forces that make it spherical in the first place. While it was out of shape, the forces that normally force it INTO shape, well that energy was being expended directly against you. When you stop accelerating, it becomes a sphere once more.
All matter has dimensions and would resist your attempt to change it's shape .....and your attempt to change it's shape is resisted in more or less the same way.
If I pushed an atom of hydrogen, I imagine I would throw the sphere of the electron path out of shape and out of "center" with the proton and the weak EM force would be acting against me to resist my attempt to do that.
It requires no relationship with other matter or with gravity as far as I can see.
My theory would hold if the soap bubble and I were the only matter in the universe.
Well there's my thoughts, such as they are
From others, I would appreciate an explanation about why I'm obviously wrong apart from the fact that I don't have a PhD. PM me if you don't want to bore the whole room
Addendum: Perhaps if this much is obvious, the next question is: why does the bubble flatten? Why does the opposite side of the bubble resist thereby causing the change of shape? Well that has to be a function of time and the elasticity of the mass in question. If you imagined a line of dominoes across the middle of the bubble, you can see it takes time for the acceleration on one side the bubble to be experienced by the other. The more elastic the mass, the longer it takes for inertia to be experienced by the accelerating body (luckily for pole vaulters) and the longer it takes for the body to change it's vector accordingly.