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Indeed, peoples' bodies (and brains) are not reliably symmetrical... so it is reasonable to not necessarily have the left and right parts behave identically. Not only for drums, but also keyboard, especially more classical piano (familiar to me). The roles in the latter are not symmetrical, besides! :)
Yes, and I do suspect that for both singers and instrumentalists, if you notate it in a "not-pushed" way, but suggest that it be pushed before the beat, they'll find it easier to read to perform, ... as opposed to deciphering (if sight-reading...) the relatively complicated dotted/held stuff as, in the end, just meaning to push the beat.
Yes, perhaps the original question's form was slightly misguided, seeking to make-more-perfect something that was not the actual goal... "Bigger picture" is very often the correct re-framing/answer to a naive question.
Again, yes, listen to recordings... In particular, also, note that whatever tempo is chosen, the pros will not sound rushed... which would be antithetical to that "cantabile" indication. So, surely, however fast you decide to play it, you'd want it to sound like you're in control, not rushing. :)
Yes, I'd emphasize the voicing aspect: stacked triads, for example, are just one choice of voicing... definitely not in the contemporary jazz idiom, whose internal intervals are more often fourths or tritones.
As a pianist, it looks completely readable to me... Can you clarify the issue that you see? Is it the slightly funny shape of the beam in the first part of the second measure? I didn't even notice it until I was trying to imagine what one might object to...