No, the Cavendish experiment measures the force of gravity between heavy balls. It's got nothing to do with the location,
Correct. This does not mean location was not a variable.
and, in the most accurate experiments, all the other variables you mentioned have been accounted for. It's not impossible to remove the variables. It's relatively easy. All you have to do is make sure that it is reasonably far away from any changing source of gravity. Cavendish wasn't even in the room where the apparatus was. He observed it using a telescope, so that his own mass won't affect it in the slightest.
Did he perform it in intergalactic space, away from the gravitational field of the Earth?
Again, I am not saying UA or the weak-gravity etc model are accurate: I'm saying it is premature to reject them utterly, beyond all hope of refinement, when responses may always be found.
There are many inconsistencies with your model, which I'm not going to address right now, and the amount of "refinement" that would be needed is... Well... Let's just say that you would need something that is completely different.
It's not my model. My model is still in development; I am simply examining all possibilities. I do not favor UA in the slightest, as I have said numerous times.
A claim is not fact. You do not know evry possible refinement, you can not simply state that there is no reasonable application of it.
You also have to take into account the Occam's razor. I mean, if you're going to substitute every known law of the universe for something completely different, why don't you just say that the earth is flat, but even if you go to space and take a photo of its curvature, it's not proof that it's round, because there is some sort of law that makes it appear like it's round? Why not just say that it's a law that the earth must be flat?
Aside from your rather absurdly extreme case, there is a difference between replacing and substituting. If I came up with a model which replaced every law of the universe in a way that was fully supported by observations, and which explained everything, and required one less assumption,
this would be preferred by Occam's Razor.
The key point of Occam's Razor is 'all else being equal'. You don't start applying it from the status quo: of course such a model would depart greatly from what's currently accepted. That doesn't mean there is nothing else that could explain both modern and ancient observations and results: to make such a claim is unscientific. Science fully allows for old theories to be replaced.