I'd look at using an SSH reverse tunnel. If you can connect from the plex-server to a server hosted on EC2, Linode, DigitalOcean, etc, you could expose the service from that.

Something like:

       ssh -f -N -T -R 8080:localhost:80 [email protected] 

Now access to your remote host on port 8080 will be mapped back to your home machine, behind the NAT. You could install nginx as a proxy for it, etc.