apparently there is a ton more data they can see using their diagnostic tools when the device is a TWC modem vs. one I own
Not true, they can gather all the data they want from any provisioned cable modem on their network, regardless of ownership. They may CHOOSE to only gather data from the TWC-owned modems, but that's their choice.
You will want to put the DG1670A into bridged mode so that it only acting as a cable modem, and use your own router to manage your home network. Depending on how they (TWC) have set up your DG1670A, you might be able to put it into bridged mode yourself, or you might have to get someone from TWC to do it for you. See if you can access the internal web server at 192.168.0.1, username=admin, password=password.