I have listened to both of the extracts you posted and I fail to hear very much, if any, difference between the two! Yes, the second has clearly been made "louder", but, to me at least, it does not sound "distorted". So, inevitable question: what are you using to listen to the two extracts? Is it possible that, whatever it is, those "loud" sounds are actually causing the speakers/headphones/ear buds/whatever you are using to "distort" because their drivers are being overloaded? I even downloaded your files and opned them in Audition CC (latest version) and still could not really hear anything I would even remotely term "robotic distortion". However, what I did notice in the spectrum analysis window is that you have quite a lot of sub-150 Hz "noise". (See the attached screenshot). Listening to just that frequency range, there is what sounds to me like noise from your mc stand; I think ACX will require that to be removed. HTH
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