This year at Kentucky Music Week I'll be teaching a class in what I call "Dronal Fingerpicking." Since many people associate drone and "dronal" with traditional strumming styles, I have always used these terms to refer to the use of open or unfretted strings -- whether you are strumming, playing single strings fingerpicking-style, or playing single strings with a flatpick.
I have simplified most of my playing greatly over the past couple of years, trying to get to some of the essence of the mountain dulcimer. Sometimes, a melody sounds best when it is allowed to be almost totally alone: stark and plaintive. Then, with the occasional addition of a supporting open string, you get a sense of fullness and richness.
This alternation between the single string melody starkness and the fuller melody supported by open string --- makes for a nice diversity in texture. Make sure to add some expressive dynamics (playing very soft sometimes, sometimes building in intensity, and sometimes playing as loud as you can), and this will make your performance really come alive.