I did not receive any feedback about my problem and the NTFS volumes. However, I was able to work around this by simply making the Ubuntu user that logs in to be the plex user. This way, when the drives are mounted as the default system user, the plex user has permission. I simply reinstalled Ubuntu on this computer with a simple install and small footprint for my media server installation.
Not sure if this will work for others with a similar problem, but it did get me around my problem for now.