So I gave up. It seems no one knows what the problem is (including me ) I switched to the Plexinc container and finally got back up and going.
It took me quite a while to get it all working, so If anyone else needs to make the switch here are a few tips from my past couple of hours of pain:
First take the time to copy your binex-plex config directory to a new location, so you can keep the original for reference in case you screw up and need to do it over.
Next, read and understand as best you can, the readme for the Plexinc container: https://github.com/plexinc/pms-docker
The /config directory for binhex-plex docker has the directory "Plex Media Server" directly inside it.
In the Plexinc docker, the "Plex Media Server" directory is inside "Library/Application Support/", so you'll have to create the directories "Library/Application Support" and then move your existing "Plex Media Server" into it. Your /config container path should then point to the directory containing "Library"
If this sounds confusing, you can always just create a temporary plexinc docker with the container name "plex-tmp" or something, start it up with the default values and look at what it creates.
In the directions don't forget the variable ALLOWED_NETWORKS, otherwise you won't be able to connect to plex on your local network.
If you have a plex pass, the repository field should be 'plexinc/pms-docker:plexpass' instead of 'plexinc/pms-docker', so you receive updates correctly.
For more tips, 'Spaceinvader one' created a video on switching containers that's also worth a watch: https://www.youtube.com/watch?v=7RgPx7BN8DE
Hmm... I think that's about it. In any case that's what worked for me. Good luck!