Your model is nonsense before we even try to test it against empirical reality because its units do not stack up. The left hand side of your equation is force. Force is:The gravity model F=(M+m)²/r² has a nonlinear relationship between force and calculable mass. It works perfectly for modeling gravity but the concept of mass is just different than the one you are used to.
F = mass * distance * time^-2
Your right hand side = mass^2 * distance^-2
m * d * t^-2 =/= m^2 * d^-2
Your right hand side lacks any time units for starters. Your equation would only make sense...if you add a constant that balances up the units being used.
You need to add:
d^3 * m^-1 * time^-2
We will call this constant a Humble (H) in your honor. Or will we? Its the same units as G!
And funnily enough, your equation will finally make sense as a coherent hypothesis but still won't match reality.
Not only do you fail in your quest to demolish G, the only real difference left is your prediction that force will vary according to (M + m)^2, all else being equal, whereas Newton predicts it will vary by Mm, all else being equal.
Since Newton's predictions have held up as close to reality under intense scrutiny and your prediction is significantly different even after I fix your equation (and made no sense at all before)...
Your hypothesis (even after I fix your schoolboy unit errors), is falsified.