I also think that the stitch you are using could just be a stiff stitch. I just recently completed a lengthwise scarf which you can see at the bottom of this post
and the stitch I used on it is the woven stitch. It came out firm but still drape-y like you want a scarf to be, not stiff like a board!
So perhaps finding a looser stitch would loosen up the feel of the scarf.