As far as another option, you can buy your own modem and install it with the TM3402. You'll just have to call Cox to activate your new Internet modem..
I had the TM3402 as an all-in-one device for my services but it started fumbling with connectivity. I still had my previous DOCSIS 3.0 so as an interim solution, I installed it alongside the TM3402. TM3402 was for telephone; D3.0 was for Internet. It worked. Internet service was great so I prolonged replacing the TM3402 for another all-in-one device.
Two years later, Internet service has still been great and I haven't had any issue with it. I only have the 150 Mbps plan so the D3.0 is good enough.
As long as your potential Internet modem is on the Cox Approved List, you should be good-to-go.
www.cox.com/.../cox-certified-cable-modems.html