Huh.
The machine is using NetworkManager, there shouldn’t be an eth0 let alone an eth0.0
As far as I am aware, there ought to be 3 networks on that machine on two ethernet cards. The 10.1.x.x network is a 10-gigabit link to the house etc. And for legacy reasons there’s also a 192.68.1.x network on there too.
The 1-gigabit link is a fiber connection to the outside world, and uses the 63.x.x.x ip, which is public and ought to be firewall-free at the router, it depends on the firewall on the plex server itself for protection. There ought to be no other ip alias on that public address for pretty much the reason you mention - originally the 192.168.1.x network was on there, and AT&T’s (useless) router was getting confused because it doesn’t seem to like multi-homed machines, it interferes with the auto-machine detection it uses.
So, I just checked, and I have two ethernet interfaces (discounting the virtual bridge and loopback):
[simon@lyonesse ~]$ ip a
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000
link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
inet 127.0.0.1/8 scope host lo
valid_lft forever preferred_lft forever
inet6 ::1/128 scope host
valid_lft forever preferred_lft forever
2: enp43s0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP group default qlen 1000
link/ether 00:d8:61:76:42:92 brd ff:ff:ff:ff:ff:ff
inet 63.x.x.x/28 brd 63.y.y.y scope global noprefixroute enp43s0
valid_lft forever preferred_lft forever
inet6 2600:1700:5450:46a0:c22c:2ec3:bb9c:5653/64 scope global noprefixroute dynamic
valid_lft 3567sec preferred_lft 3567sec
inet6 fe80::c6a3:a5bd:e485:30aa/64 scope link noprefixroute
valid_lft forever preferred_lft forever
3: enp36s0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP group default qlen 1000
link/ether 00:d8:61:76:42:93 brd ff:ff:ff:ff:ff:ff
inet 10.1.1.2/16 brd 10.1.255.255 scope global noprefixroute enp36s0
valid_lft forever preferred_lft forever
inet 192.168.1.180/24 brd 192.168.1.255 scope global noprefixroute enp36s0
valid_lft forever preferred_lft forever
inet6 2600:1700:5450:46a0:1ee2:14b3:8d8d:68e3/64 scope global noprefixroute dynamic
valid_lft 3567sec preferred_lft 3567sec
inet6 fe80::6ef9:d92:4b1b:fbf0/64 scope link noprefixroute
valid_lft forever preferred_lft forever
4: virbr0: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc noqueue state DOWN group default qlen 1000
link/ether 52:54:00:e3:95:e0 brd ff:ff:ff:ff:ff:ff
inet 192.168.122.1/24 brd 192.168.122.255 scope global virbr0
valid_lft forever preferred_lft forever
5: virbr0-nic: <BROADCAST,MULTICAST> mtu 1500 qdisc pfifo_fast master virbr0 state DOWN group default qlen 1000
link/ether 52:54:00:e3:95:e0 brd ff:ff:ff:ff:ff:ff
So you ought to be seeing enp43s0: (public IP) and enp36s0: (private ip’s). I also intentionally set no default route on the internal network, so the default route for all traffic with a destination that can’t be immediately satisfied is via the public ip gateway
[simon@lyonesse]$ netstat -rn
Kernel IP routing table
Destination Gateway Genmask Flags MSS Window irtt Iface
0.0.0.0 63.x.x.x 0.0.0.0 UG 0 0 0 enp43s0
10.1.0.0 0.0.0.0 255.255.0.0 U 0 0 0 enp36s0
63.y.y.y 0.0.0.0 255.255.255.240 U 0 0 0 enp43s0
192.168.1.0 0.0.0.0 255.255.255.0 U 0 0 0 enp36s0
192.168.122.0 0.0.0.0 255.255.255.0 U 0 0 0 virbr0
The machine that used to be the video server was not running NetworkManager, and that one did have eth0 and eth0:0 - is it at all possible that the config is confused ? If you recall, I did a “swoopy” transfer of the database from that machine to this.
For what it’s worth, according to my firewall log, the last time the WAN went down was:
2019-08-01T07:13:46-07:00 network unavailable, WAN down
and it was only down for 2 seconds. Before that it’s been up as far as the log goes back ( a month or more). Plex has lost its connection a lot more than that.
In an effort to help plex out, I just configured the LAN networks on the Settings → Network tab, but it didn’t make any difference to the problem, which still shows the version with the missing shows 
One final thought. I just restarted the server…
[root@lyonesse]# systemctl restart plexmediaserver
but it made no difference. Then I clicked to uncheck ‘Treat WAN IP as LAN Bandwidth’ on the Settings → Network tab, and refreshing the ‘Movies’ page got all my shows back again. Maybe another coincidence.