Custom binding can do the job for you, here is the updated fiddle :
http://jsbin.com/edopuh/3/edit
For excluding any particular li element from sortable element you can use items option of jquery ui sortable plugin, it accepts jquery selectors.
Update
For doing something after moving item you can use Update event of jquery ui sortable. Check this updated fiddle, in this fiddle after moving item you will get the alert :