Daniel15

My knowledge was a bit outdated. Making the changes to the extra parameters should still work, but you can actually do it in the UI now without going to advanced mode: Select "Container" for network type, then the right container for "Container Network"
 

 
If that still doesn't work, please provide the error message

I figured out that there's an "Interface Rules" section in the network config that can bind particular interfaces to particular names, but it only appears if there's multiple NICs in the system. The two onboard NICs were bound to VFIO, so there was only one NIC in use with Unraid, and so I didn't see this section.
 
I was able to unbind the two in-built NICs from VFIO via "System Devices", reboot, update the Interface Rules to set the 10Gbps NIC's MAC to "eth1", re-bind the built-in NICs to VFIO, reboot again, and the 10Gbps NIC remained as eth1 on the next reboot. I'll see if it works long-term.