OK, on creating a VNET correctly, I have resolved the issue. For others with the same problem, the commands I used to switch the jail to using a vnet were as follows:
iocage set vnet=on plex
iocage set ip4_addr="vnet0|192.168.1.2/24" plex
iocage set defaultrouter=192.168.1.254 plex
I also needed to add the following tunables under System>Tunables:
Variable: cloned_interfaces Value: bridge0
Variable ifconfig_bridge0 Value addm igb0 up (note that you may need to replace igb0 with your specific network interface
After making these changes, plex now works perfectly, meaning that the issue was probably to do with not having access to the full network stack
