I have this same thing happening. I'm not going to add any moss to mine. I think originally the moss helped the plant and protected it until it got situated and started to attach itself to the mount.
I think (only my opinion) that they truly like hanging out in the breeze like o'natural. As long as they have a good flow of air, good humidity, and are fertilized, I'm leaving mine alone. I think it looks soooo cool.
