E4200 - How To Get Centurylink Connectivity

At it's most basic, here's my network.

Wall --> TP-Link 8616 ADSL2+ modem (not sold by Centurylink) --> Linksys E4200 router --> desktop PC wired via ethernet.

There are other devices, but I remove them and disable wireless when I'm testing. I sometimes remove the router from the equation as well.i'm on CL's 12mbps service, which means that I should be seeing approximately 10.2mbps down (DSL is typically 85% of advertised). Most of the time I get about 10.4mbps down. However, about once every 3-6 weeks, speeds degrade to about 4-7mbps and remain there. Rebooting the router/modem does nothing. I will call CL, and they will tell me that the problem is my modem, that I need to buy one of theirs. I ask them, for shits and giggles, to reset the connection on their end. I then simultaneously kill the power to my modem/router. When everything is back online, I'm back to 10.4mbps. The rep tell me that my connection is fine on their end and that the problem is still my modem. This will occur again in another 3-6 weeks. I often get the same rep.