Wow, Tier 1 by phone is getting pretty bad. The T3 errors are from noise/ingress on the upstream. I think the T4 errors are from you somewhat low downstream SNR but I am not sure. It should be above 35-36 but you power level is on the high side. Are you going through a amp or splitter of any kind? If you have a direct connection I would demand a tech. As long as it is a outside problem there should be no cost. If you are really worried, get Cox Complete Care for a few months to cover the cost.
Bull poop. They are just pretending they can't roll a tech. Email Cox at email@example.com and ask. Include your account info and a link to this thread. Update the thread with what they say. If they keep being difficult, file a FCC complaint but I think that is extreme at this point. Try the email first.