So I've done some rewiring and so far no issues, and I haven't replaced the modem. Outside of this one issue (which apparently wasn't really cox's fault) I've been generally pleased with the service. The speeds have been as advertised or better, and until recently it had rarely been unreliable. BTW the firmware for my modem was automatically updated last night around 1 am, which I suppose the timing must have been a coincidence. As I mentioned I had purchased an SB6141 as a replacement, but I will likely return it if my connection holds steady. I thought about keeping it anyways since I think in the not-too-distant future we'll see 100 mb/s speeds (and beyond) which would eventually require 8 channel bonding.
I guess you can chalk Cox customer service as a success since my problem was eventually resolved in a reasonable amount of time. That being said, some of the poor advice I was given (buy our protection plan, buy a new modem) would probably direct me to the forums instead of calling with any future issues.
Thanks again to everybody that helped.