Okay, here's the issue then: The thought experiment I posed makes perfect sense to me and your logic seems a bit fuzzy around the edges ( and visa versa ). So that's where the disconnect is, which means we need to explore this deeper to get to the bottom of it. I'm not saying that Newtonian formulas are more accurate, so that isn't the issue. I have no problem with the analogy of space curvature to make more accurate predictions. I have an issue with assuming that because the analogy works, that space is actually curved in reality on an intrinsic level. So let's set any debate about Einstein ian and Newtonian math aside. They're not relevant to the issue.
We can simply substitute any sort of equation, the point being that equations are abstract mathematical constructs that exist only in our mind. That makes them ideas, not realities, and the question of whether or not space is actually curved is an existential question, not an abstract one. So let's accept that as the initial premise.
When we do that, what we have is an abstract representation ( math ) that describes accurately the behavior of objects in space. The point of contention here appears to be that some people ( including yourself ) make the leap in logic of equating the abstract with the existential ( that because of the math space itself must be curved ). There is no evidence for this. There is only evidence that things in space behave according to the predictions made by the math ( abstract ). But space itself ( existential ) appears to be uniform.
The logical proof for this is in the types of thought experiments I mentioned. To reiterate. Gravitational lensing can produce two images of the same distant object. Obviously these cannot be the same object and two different objects at the same time. Therefore what has happened is not that space has warped into two separate "spaces" with two separate objects. It's simply the way light from the object has been bent around massive objects.
Similarly, as pointed out in the initial example, if the apparent position of an object and the actual position were due to the curvature of space, then the direct route to the object through space would have to be through curved space, or else to tunnel through the curvature in a straight line. But we know we don't have to tunnel through the curvature. We can simply calculate the actual position and plot a straight line through space.
Therefore, you have two logical reasons with practical applications that prove ( logically ) that space itself ( existentially ) must be uniform, even if the curved space analogy works for predicting the behavior of freely moving objects ( including photons ).
Interesting, but again, none of that is relevant to the point I made. We're only dealing with the issue of the abstract versus the existential. I'll close by also reminding you about the example of the equivalency principle, another analogy that is clearly not the case in reality but forms the basis of Einstein's gravitational theory: Equivalence principle - Wikipedia
So my feeling on this is that perhaps we had our premise wrong at the outset and you've been trying to prove the case that Newtonian math isn't as accurate. I never had a problem with that in the first place. However let's not confuse the abstract with the existential. By keeping them separate we can both be right without any conflict in the bigger picture.
