Cox does support DOCSIS 3.1 and it’s what they use for Gigabyte speed. The Arris/Motorola CM8200 is also a DOCSIS 3.1. I am having similar issues and I believe it’s the hardline running into my house. The line into the house was recently replaced (year ago) so it leaves the hardline as the primary issue.
I "upgraded" to Gigablast two weeks ago. It took 10+ phone calls before a helpful tech came out and told me that Cox would never tell me over the phone that the problem was their fault (they never entered the S/N or Mac ID to activate my modem), but the issues I was experiencing were entirely on their end. Now that it is set up, I can get online, but I can't hold a steady connection and has made online gaming nearly impossible. After reading a lot of these posts, the ping spikes that we are experiencing are likely on Cox's end as well.