Have you done a trace to show if the packet is still reaching it's destination? Networks are designed to manage their traffic so they can/will drop ping/ICMP, either by default or sometime intermittently because of traffic. I say drop, but that isn't the right work because they still send the packet to the next hop, they just either block or don't send the return packet to you, so that request times out. Pingplotter is a great program to use and they have documentation on this effect under how to read their results. I don't fully understand much more then to know it's a thing. ICMP de-prioritization but it has other names and other things are also probably playing a role, even if the core issue is on Cox's end.
Also, you haven't commented on the fact that at least one error you getting points to a issue with the OS/device. Do you see this occur on other devices on your network or connected directly to the modem? I get that it's frustrating to be gaslighted by tier 1. That all they seem to do is tell you to reboot you modem, but the way you get around that here is to think of any questions one would have about your situation and present them as part of the post with any answers/data you may have on them. Blaming wifi is reasonable if you have not given the data that you have removed that as a variable. Most people use wifi, only wifi, but have no idea how wifi works, or sometimes that they are even using it. So the right first question when someone says are having intermittent connectivity is to ask if they are on wifi. Second connect direct to the modem with a different device. Third is to look at signal levels/logs/diagnostic data. 4th is to double check physical layer. Connections, wires, etc.