I think your way of arranging it works pretty well overall. I agree with what Static mentioned about m. 20-32 about there being lines above the melody anyway, and pulling it apart like this allows the arrangement to lay everything out without too much difficulty.
For m. 37-44, I prefer what you already have in the sheet vs. your screenshot above. In measure 37-40 you keep that overlapping call-and-response between the two lines without ever confusing them or omitting part of them, and the left hand part is pretty easy to play. In your screenshot above, the melody in m. 41 gets obscured in m. 42-43, and it's much more apparent where the layers are differentiated when they're far apart.
In regards to how some of the chords sound ("vertically"), I think 42 sounds fine personally. The one place that does bother me is m. 24/32, the Ab/G/D/F sounds rather dissonant, and probably part of that is because the Ab on bottom is sustained as the harmony changes but is restruck at each measure here. Maybe it doesn't sound as weird when played at full speed, though.
Unrelated, m. 31 sounds rather empty compared to the more colorful chords around it, with only the root and fifth. Might be worth making a small adjustment to fill that out even if the original just plays those notes?
That's all I had really, I looked it over and everything seems fine accuracy and presentation wise
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