It's likely that there have been bottlenecks, where a single written version became the main common ancestor to copy from. Long after the oral tradition died down and other written versions were lost. Or because some patron decided to fund the dissemination of a particular copy, like Guttemberg or King James, or the Toledo School of Translators. Or because a particular heir of the oral tradition wrote it down, like Homer.

It doesn't necessarily mean that the story was stable, it's just the version that got to us.

What you are saying is generally true (and certainly true for many Indian texts), but the oral tradition of the Vedas really is old. Having been brought up in the West I only learned enough for daily and occasional rituals. My guru taught me without looking at a book and although I have such books now I bought them for curiosity only; if I had a question about recitation it would not occur to me to consult them. My son has learned the same way.

Could be but all across different regions across the subcontinent where the Vedas are orally recited, except for some technical tones and notes (which is the mechanical part of Vedic Sanskrit) there is little difference.

There are serious attempts made to write down the vedas. The thing is, historically, very few people learned all 4 vedas by heart; Instead different families recited very small part and passed the recitation as heirloom.

If you meet all those families and compile their recitation, it exactly matches to what we have from different earlier efforts of canonisation.