Soft bodies are definitely not the answer - the stretching and crinkling will not go away. You can tweak the hell out of it but you'll only get close. Here's a suggestion in the form of a rigid body exercise; you can apply the concept to the tassel ...
Create a sphere and orient it so the north/south pole rests on the X axis. Raise it up several units in Y, and view it in the front window. Create a rigid body out of it.
Duplicate the sphere and translate it in X so that there's about one unit between the two spheres. Duplicate it 3 or 4 more times in the same fashion. Create a gravity node, connect all spheres to gravity.
Add a nail constraint to the first sphere. Select the first and second spheres, add a pin constraint to them. Add pin constraints to 2&3, 3&4, 4&5 and so forth. Click "play". You should have a chain swinging and twisting with gravity, nailed to the viewport via the first sphere. Rewind the scene.
Select a single "latitude" isoparm from each sphere sequentially, and loft them together. Turn off the visibilty of the spheres. Press play. That's your tassel.
I find that it twists and bounces too much, but you can fix that by adjusting the damping value of the sphere rigid bodies. I'd suggest a higher damping value the closer you get to the hat edge.
When you build the mortarboard, you can build the tassel by duplicating the isoparms and translating them so the lofted surface extends to the center of the hat. Instead of nailing constraining the first sphere, you can make a passive rigid body out of it and group it to the mortarboard and offset it so it rests on the edge.
Good luck
D