you could you try to do the cell fracture after subdividing the mesh… do it on a highres mesh. that low res mesh fracture will not work when apply a subdiv after cellfracture. subdiv will allways cause that holes and maybe do the solidify after fracture.
another thing you could try or think about is to play with creases for the charts edges in edit mode to use a subdiv… did not do that before but in that case it maybe works.
dont know if thats much of help but maybe gives some ideas.
 another reason for that big pieces that you are missing can be that your mesh has some extra loose parts or holes or whatever. try to keep the mesh consistent.