This is yet another example of why I carry a couple loop runners on speedline carabiners. On that limb I would use the loop runners instead of half hitches or pulleys, then just clip them onto the lowering line. It doesn't keep the limb together so much, but it would catch the big pieces and keep them clipped to the lowering line.
Or, if you were piecing the limb down, they would replace the pulleys (but much faster and easier to set and retrieve).