You are having basic permission and ownership problems as Bob stated.
The reason Plex can't read below a certain point is default linux permissions. The linux rule states that one unprivileged user (plex) cannot see another user's files (what's in your home directory) without express 'read' permission being granted. Directory read permission is in two forms. 'r' is to read the names of the files in a directory, 'x' is to descend through it (get to a subdirectory or file within the directory). File permissions are simple 'r' (read the contents). 'x' is not needed for files since we don't 'execute' media.
I must first ask if Plex is indeed running as user 'plex', in group 'plex' and if it was started at boot (as a service) or if it was started by you. Plex should be running as itself, not under your username.
Take Plex out of any groups you've added it to. It serves no purpose. Take yourself out of the Plex group if you've added yourself to it. It also serves no purpose. Plex should be free-standing in its own group and none other.
Presuming this is settled and Plex is indeed running as required, the correction to your linux filesystem permissions are very simple. They presume your username will remain the 'owner' of the media. Plex will be granted Read permission to the files and directories containing your media. This is its minimal requirement.
I would recommend you naming your media storage directories to exclude your username from the path. I use /media/movies, /media/tv, and /media/music.
You could achieve this with /media/storage1 and /media/storage2. Care must be given to not have TV series and Movies intermixed as the scanners for each library type will get confused. (The movie scanner doesn't like scanning TV series names, etc)
if your movies and tv programs are contained in directories /media/storage1/movies, /media/storage2/movies, /media/storage1/tv and /media/storage2/tv, Plex will find this very easy to navigate and maintain properly.
I will presume, for the rest of my reply, your top level media directories are structured as I outline here.
This will permit you to retain ownership, which you may set back to you as the owner ('chown -R peter /media/storage1 /media/storage2') to ease managing your media.
sudo find /media/storage1/movies /media/storage2/movies -type d -print -exec chmod 755 {} \;
sudo find /media/storage1/movies /media/storage2/movies -type f -print -exec chmod 644 {} \;
sudo find /media/storage1/tv /media/storage2/tv -type d -print -exec chmod 755 {} \;
sudo find /media/storage1/tv /media/storage2/tv -type f -print -exec chmod 644 {} \;
Lastly, your fstab entries for the two drives should be basic entries. Edit appropriately for your device/partition names:
/dev/sdc1 /media/storage1 ext4 defaults 1 4
/dev/sdd1 /media/storage2 ext4 defaults 1 4
Restart plex or reboot as required.
When restarted, add movie section for directories storage1 and storage2. Repeat for tv section.