I finally figured out how to achieve the coloring without the use of Reconcilers.
I discovered that first I needed a way to obtain a reference to my SourceViewer object, as I am extending TextEditor. I also discovered that I could implement the TextListener interface and add my own listener to the SourceViewer object. One must be careful, however, as calling the getSourceViewer() method can result in null if not called at the appropriate spot. Originally, I overwrote the init(...) function in my editor class and made the getSourceViewer() call, but it still resulted in null. After doing a bit of research, I discovered that I could properly obtain a reference to the SourceViewer object by overriding the createPartControl method. I first call super.createPartControl(...) and then make a call to getSourceViewer(). After I obtained that reference, I used that with my listener class I created and was able to do the coloring myself with the setTextColor method the SourceViewer object has. Hope this helps others in the same situation.