I figured it out. I still had 127.0.0.1 set in a couple of places.
I had to change the IP address in the following locations:
Database:
auth.realmlist.address and auth.realmlist.localaddress to 10.x.y.z
bnetserver.conf:
LoginREST.ExternalAddress=10.x.y.z
LoginREST.LocalAddress=10.x.y.z
Client:
World of Warcraft\ _retail_\WTF\Config.wtf
SET portal "10.x.y.z"