Open-mindedness is not a virtue when one wants to simultaneously claim to be a scientist but also to ignore the data.
You claimed that at one time tests of GR were taboo. I pointed out that these tests have been performed for decades, and asked you when this time was. You did not answer.
You speculated that there was some sort of deviation from inverse square, and some sort of non-universality of free fall, and some sort of exotic matter. None of these have been seen. The paper you pointed us to doesn't support this - it shows these effects are so small that our uncertainty on the value of G is 100x larger.
1) GR was never "taboo." Just like any other theory (or model) it must be tested. Otherwise it is as good as math homework.
2) I already made a note as to Cavendish's intent. The by-product was the constant G. Dozens and dozens of experiments measuring G have been conducted by national standards groups and university groups around the world. I say dozens because there are a number of ways to measure G. Oddly enough they all agree fairly well, except for the German standards group. They only measured G to three sig.figs. because their apparatus was leaking.
Mammo, you can continue arguing about
a) entropy induced mass change:
Recall mass is not influenced by thermodynamics with the caveat that there is no mass-energy conversion and that your Gaussian sphere still covers the point in question
b) logic errors with Cavendish's experiment:
this has already been beaten to the ground
c) changes in gravity due to what you read in physics texts:
Keep in mind people have told you that Newtonian models work well for slow moving reference frames; GR for frames that suffer massive distortions.
Nevertheless, G is still the same for all matter and energy densities. No evidence has indicated that G should be different, this includes dark matter surveys. Even anti-matter corresponds to G.
So unless a breakthrough in physics happens (maybe it will be you) arguing things like logic errors in a thoroughly hashed experiment and truth behind gravitational shielding are superfluous.