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I've solved my own problem. Basically this stems from my unfamiliarity with Anaconda/Miniconda and the condas environment. I had to create a new environment and was able to install the packages into that new environment.
conda create --name YOURNAMEHERE python=3.6
This will create a new environment with your environment name in C:\Program Files\Alteryx\bin\Miniconda3\envs\YOURNAMEHERE.
NOTE: It will complain about a space in the path due to it being located in the Program Files directory.