The perspective effect used to tilt the ball upwards to can match something that is already tilted upwards by another mechanism. The method you provide with the ball is unable to distinguish between the two.
I don't know what you mean by "another mechanism". The phase we see on the moon is because of our perspective. You have shown that with your experiments with the ball. As you take the photo from different angles you see different "phases" on the ball. In real life the ball is always half lit and half unlit, but the "phase" you see depends on your perspective. With a ball close to you it's easy to change your perspective. Because the moon is so far away that it doesn't matter where you are on earth, your perspective is effectively the same. That's why we both see the same phase at night despite being thousands of miles apart. You'll only see the same phase on the moon and the ball if you line them up correctly so you are looking at both from the same perspective. I have drawn diagrams which explain why. That is the point of that ball experiment.
Since you posted "Yes", you acknowledge that this is a faulty experiment which proves nothing.
Please stop the straw man trolling.
It's not a faulty experiment, the issue here seems to be that you don't understand what experiments are for.
They are generally designed to test a hypothesis. They don't "prove" the hypothesis, they can only disprove it. For example.
Let's say I have a hypothesis that things fall to earth when I drop them.
I design and run an experiment where I drop things and sure enough they all fall. Hurrah, hypothesis proven!
Well, no. Because then I publish my results and someone else "drops" a helium balloon and it floats away. My hypothesis has been shown to be incorrect.
My original hypothesis was too simplistic. A more accurate model which explains observations is that gravity exerts a force on objects, but other forces may be acting too. In the case of the balloon a buoyancy force is acting which is stronger than the gravitational one so instead of falling the object rises.
That's how science works. Nothing is ever proven in the strictest sense, but the more experiments which are run the more confidence is built in the underlying hypotheses which they are designed to test.
In this case I hypothesise that:
1) The sun is illuminating the moon
2) Light goes in straight lines.
IF those two things are true THEN a line perpendicular to the terminator I observe on the moon should point at the sun. When I see the moon tilt illusion it appears that this is not the case.
The string experiment demonstrates that this apparent misalignment is simply an optical illusion. It proves there is no misalignment, it doesn't prove the hypotheses but it isn't designed to.

Now. What you're saying is the light could be travelling like this and it would still line up with the string:

You are correct. But what evidence do you have that light behaves this way? The light could be doing this too:

That would also line up with the string. But, again, I have no evidence that light behaves that way. I do have evidence that light goes in straight lines. LIGO has 4km long straight tunnels and bounces a laser between mirrors at each end 300 times making an effective distance of 1200km.
https://www.ligo.caltech.edu/page/ligos-ifoYou would have thought that if light was being bent they'd have noticed.
So while the string experiment doesn't prove the light is going in straight lines and it could be going along the path you suppose, that just isn't how light behaves.
In RE light travels in straight lines,
In FE light is bent upwards by EA.
The path you claim is possible for the light to be travelling in doesn't match either RE or FE, it is a complete contradiction to EA.