The cracking of the surface can also be caused by getting the dirt to wet and letting it dry to quickly. Try covering the areas and letting them sit over night. The cracking is from the dirt actually shrinking for the shape you formed it in.
When hand tamping wet dirt you need to let it sit so the water soaks in. The deeper the water has soaked in the more you will be able to tamp the surface. Also get an old piece of carpet lay it over the jump then hand tamp it. You will be able to tamp when the dirt is wetter and get a harder surface. Old carpet is a must for really getting well tamped jumps.