Do you use a base add-on type like TukUI, ElvUI, or DuffedUI? If not, I heavily suggest you get this overall add-on UI. It provides what you are looking for by putting your DoT icons above targets' heads. I use it when playing Affliction by tracking Unstable Affliction, Corruption, and Bane of Agony. I believe Tidybars is another add-on that allows the use of DoT icons to appear over targets, but I've fallen too much in love with the TukUI family. The guys at Icy-Veins play with ElvUI, and once you see it, you'll understand why. I can take a screenshot or two of my UI when I get home to show you how the multi-dotting tracking works with DuffedUI.
A gameplay tip is to never change targets by clicking things unless you are changing to something more than 30 yards away. Use your Tab key to switch through targets to shave off tenths of seconds on your DoT application time.