I just added chaeto to my fuge. I did some reading on it and most people recommend that it be placed in a fuge with a glass bottom where it can tumble freely. I had an extra chamber and so that's what I did.
They recommend as few obstacles as possible so that the chaeto can tumble, exposing all sides to the light for maximum growth. It is not supposed to attach to anything. With no current, mine did not float but slowly sank to the bottom. As I opened up the gate valve to give it some current, it started tumbling easily. It looks like clothes tumbling in the dryer.
In order to get it to tumble like that, I placed it in an empty chamber in the fuge. Water from the first chamber spills over a dam and flows down into the chaeto chamber. Then it gets sucked up into a U tube siphon on the other side creating a very effective swirling motion. I must be bored... I bet I stared at my chaeto tumbling in the fuge for 30 minutes! ***)