You need to step back and identify the root cause of the change.
How are you determining speed is degrading? DNS does not affect speed directly however a typical web site is often composed of many components each requiring its own DNS translation so slow DNS may affect perceived speed, but not a speed benchmark.
First step is to log into the modem and check sync speed and margin. Copper phone circuits are susceptible to noise and other interference. DSL is designed to adjust speed automatically when line degrades. Both should remain pretty stable over time. Margin may change by a dB or so but ideally sync speed does not. If your line is marginal modem and DSLAM will adjust speed to reflect line characteristics. When you reboot the modem it goes through a lengthy training period to determine line conditions. Ideally modem/DSLAM should automatically adjust speed up and down but this does not always happen, it is easier to adjust speed down when line degrades then up as it gets better.
Next perform speed test to stable sites like this one. There is a speed test on the tools page and I like to use speedtest.net.
If modem stats are stable but speed test varies it is most likely congestion within your ISPs network or that one or more PCs on you LAN is using the Internet affecting speed test. Lots of software is pretty chatty these days calling the mothership.
Speed test result should be stable based on modem sync rate. If you think there is a congestion problem try running traceroute (tracert in Windows) to stable sites like this one. Latency should slowly increase with distance and hop count. Sudden unexplained increase typically indicates congestion at that or the previous hop.
If you think you have a DNS problem might want to run GRC DNS benchmark:
I'm not a fan of using 3rd party DNS. If your ISP has an arrangement with a content distribution network (CDN) provider using other then their DNS resolver can degrade performer because it is not aware of these special connections.