Why are there omissions and discrepancies in Kaori's Kreutzer performance?
As requested, while this is not a conclusive answer, we might never know unless there is more information released.

The manga only specifies the piece, but never details the performances of the characters musically. The characters might gush over how "lively" or "beautiful" it sounds, but nobody ever talks in technical terms, much less describe sections of music.

Chapter 6 page 30-32 : The extent of description of Kaori's Performance.




Thus, we can conclude that your observations about the discrepancies in the musical pieces stem solely from the anime production. There could have been artistic/directional decisions for the eventual editing of the said pieces, such as time constraints or perhaps wanting to get a feeling across because that section or piece of music only fits that part. We might not know more unless more information is released (AFAIK) from the studio, such as interviews with the director/staff.

However, this stand does not exclude the author collaborating with the studio and affecting the said pieces. It could well be what the author had intended to portray in the first place. Again, we do not know the extent to which he has influence over the production, notwithstanding that the plot of the anime is pretty filial to the manga.

In my opinion, the "cuts" as you describe are not noticed by the general audience, and serve more as a mood setter and a plot driver than an actual portrayal of a performance. Only a more discerning and a informed listener would be able to tell that there was something amiss.