Listening to the two tracks, I think the problem is more that the snare level is high relative to the other drums. It really pops out. When I look at the track, all you see are the snare peaks, which seem to be 3-5dB above all the rest of the music. I have the snare in my MTPDK pulled down compared to the toms. Plus, they are very precise, each hit it basically the same dynamic.
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Can EZD "humanize" like MTPDK? You might try to do that on the snare drum, in addition to pulling the level down some. Drummers will vary things to keep it interesting, otherwise it can sound too much like a metronome.