We have confirmed through the changelog and through me downloading all current OC ReMixes of Gerudo Valley that the piece was never posted here. I have no idea where I may have gotten it. I looked over at VGMix, but none of the remixes of Gerudo Valley they currently have are the one I remember.
There were no vocals in the track. It had the quick little intro, then a sort of shuffling or scraping that was more percussion than melody, and then it went into the main theme.
Thanks so much for your help!