I have bypassed the router with the same result. A tech came out and replaced the buried line from the tap to the side of the house, and I have replaced the line from the side of the house, through the attic, into the room where the modem is. I still get major latency and lag spikes.
I have emailed the COX help email as suggested in the sticky, and they just keep coming back with "open command prompt and ping google.com and show us" - even when I include the full ping plotter results. My results always show that there is major latency and packet loss in the first three to four hops inside the COX network. There is either some network issues or major congestion in this area that COX can't handle.
The signal levels on the modem are good and verified by both the tech and the COX help email response, so I know the modem has a good signal - this has to be either congestion or dropping of traffic the network infrastructure can't handle or an issue with the COX network hardware itself.
https://imgur.com/a/7HXYPSi