I like decomposing the piece to understand what the author meant, and this is very effective.
I first listen to the scale once again if I stumble. Then I try to understand what chord progression the author is mostly using. This helps a lot, because you understand much better what the left hand is doing with chords, arpeggios or whatever there is.
A specific example: Bach’s Toccata and Fugue in D minor. Sometimes it’s hard to follow it all together, but specific pieces give a better insight. I understood that he’s using several scales, and the main chords or chord progression is i – iv – V – vii* with harmonic minor scale. This allows me to understand much better why the left and the right hands are doing what they are doing, even if it’s more complicated than just harmonic or melodic chords.