There aren't any default home router gateway IPs in the PingPlotter post, which is rather strange...
Are the LAN IPs in the default 192.168.x.x range or is it something different like 10.0.1.x range?
If your home router is using the 10.0.1.x range it may cause some odd issues since Cox probably uses that address space for modem management IPs. Most home routers I've seen don't block private IP address space traffic across the WAN port by default.
If you are using normal default 192.168.x.x home router LAN addressing, it's odd it doesn't show in the PingPlotter graph.--
Two is one, one is none. If it's important, back it up... Somethimes 99.999% availability isn't even good enough.