I have gone through the same exact issues. New equipment, new lines, new cat cables and yet the problems persist. I have no doubt in my mind that they are 100% cutting upload and download speeds simply because they cannot adequately handle the amount of traffic during peak hours. Please file a claim. It's all we can do at this point and if they get enough complaints they wil be forced to do something about it or risk major fines or worse with the FCC. From what I hear the new head of the FCC isn't messing around with this kind of stuff and take it quite seriously.
I cannot wait for gigabit Fiber to be available here even if its with AT&T. They really did screw the public over and we all should have access to fiber by now since most of the major ISPs took government money in the 90s to upgrade and provide reliable high speed internet to all or to at least future prep their networks for more reliable speeds and services. Instead they pocketed most of that money and left the customer to deal with the problems and lack of options.
Cox just needs to add more nodes to be able to handle more traffic. It's as simple as that.
Hope you have better luck in the future.