you can usually fix this pretty quick by turning on hidden geometry, window select the faces you'd like to give visible edges to, copy, exit group (or group original), paste in place, turn off hidden geometry, explode group..
(sometimes readjusting the soften smooth setting on the copied face after pasting.. or selecting the face and deleting, etc..).
attach the .skp if you can't figure it out.. i'm pretty sure you should be able to do it on this model.