Answer

It is important to understand that in the end the question deals only with what did or did not happen at Mount Sinai. The question is whether there was a revelation there and whether the Torah was given there, or not. The only thing that differs is the two prisms through which we examine that question: what would happen if we heard about it firsthand (that was discussed in the previous section), and whether that event was not simply an invention out of whole cloth by later generations. If the event really happened, but its description became garbled, or there was a break in the chain that was later repaired, none of that is relevant. The question is only whether at that time, at Mount Sinai, there was an event of revelation or not. Some kind of distortion, if there was one, does not cast doubt on the occurrence of that event.
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Questioner:
If I manage to convince you that the Torah in Exodus chapters 19 and 24 tells two different stories about the same event, stories that cannot factually coexist together,
how would you relate to that?

The witness argument
In our world, half a million people will "swear" to you that Rabbi Shimon bar Yochai died on Lag BaOmer—based on a mistaken expansion of an abbreviation.
Or tens of thousands will claim that the memorial day of the Bartenura is on the 3rd of Sivan, even though I know who "invented" this years ago, what his motivations were, and how much money he invested in the matter, and online you can find articles telling the story… and still people flock there!!

How should one relate to these facts in light of the witness argument?

And two more examples from the Torah
Which plague of blood was it? (see attached file)
What kind of flood was it? (see attached file)
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Rabbi:
So, then we have evidence here of a combination of two different sources. What is the problem with that?
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Questioner:
If the reliable source for the event at Mount Sinai tells two different stories, then what testimony do we actually have from Mount Sinai?

Testimony A or testimony B (assuming they contradict each other)
And then Deuteronomy comes along and recognizes only one story, and even changes that one.

So why do we have testimony at all… to A, or to B, or maybe to B1 (Deuteronomy)?

Likewise with the flood… which flood was it—one of 150 days or 40 days, one in which only rain fell or also water came up from below, one in which Noah was commanded, we would hope, to bring 7 pure animals or only 2?

That is, the testimony is disorganized and even contradictory—what kind of testimony is that?
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Rabbi:
Why is a contradiction in the details important?
After all, we already agreed that in details it is reasonable for distortions to creep in. Why does that surprise you? The question whether there was a flood or an event at Mount Sinai has nothing to do with the reliability of the details.
Ask any lawyer or judge and they will tell you that there are no two witnesses who describe an event that happened today (!) in exactly the same way.
Therefore none of this seems significant to me at all. On the contrary, if several different sources describe the same event, then it probably happened. Again, this is exactly like two witnesses.
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Questioner:
It seems to me that there are so many contradictions with enormous gaps almost throughout the Torah (also on the halakhic side, which the halakhic midrashim had to deal with) that this is testimony—if it is testimony at all—that raises a great deal of doubt….
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Rabbi:
In my view, this only means that several documents were combined here, and apparently there was no close connection between them (and that is why contradictions emerged in the tradition), but that itself shows you that there are several independent witnesses reporting the same events. True, one says the flood lasted 40 days and the other 150 days. So what? One uses the name YHWH and the other God. And therefore? At most, He is called differently in the different traditions (see at the beginning of the portion of Va'era, where this is stated explicitly in the Torah itself: "I appeared to them as God Almighty, but by My name YHWH I was not known to them"). These contradictions, precisely because they are not blurred and are visible to the eye, show that there was no kind of revision and attempt at harmonization throughout history, but rather a reliable report of several different and independent traditions, all of which point to the same essential thing (there was a flood, and there was an event at Mount Sinai, and there was a plague of blood, and there was also a plague of frogs).
As for the halakhic midrashim that try to reconcile things, on the face of it you are right. If we are dealing with two different traditions, then what is the point of reconciling them? But here too it depends on your basic assumption about the author of each document and about the editor who put them together. If the author of each document and the editor—the one who combined the traditions—were endowed with divine inspiration, then the way they were combined and the differences between the traditions do carry meaning, and then there is certainly room for midrashim that reconcile them. This is essentially something like Rabbi Breuer's thesis.
In my view, these examples only strengthen the credibility of this tradition. If there were no differences, then it would be obvious that there was an editorial hand here—deliberate and harmonizing—and then there would be only one witness, and that witness would also be someone who allows himself to tamper with the tradition. That is much less credible. The fact that there are several different witnesses testifying to the same thing only strengthens my trust in the shared core. As stated, only the core is important for the essential issue.