I may have an answer for you. Basically start at the poles reinforcing with cardstock on the inside as you work your way down to the equator. When you have two hemispheres, you can reinforce the insides with strips of thin stock and even disks slightly smaller than the diameter inserted inside. From my own experience I have found that using a copy of the parts themselves as one of the better ways to build out internal tabs to butt join the parts which gives one a nicer spherical shape. For rind cut spheres (longitudes) you want to scale them a tad smaller and place centered between the outer panels, cut into it to allow part to conform to shape. For semi-circles (latitudes), generally no rescale, but you may need to use scrap to start with the pole's tab. Engineer tabs to join the hemis together (I sometimes alternate tabs top and bottom to get them fit better)
I can draw pictures if it doesn't make sense (I had a more detailed answer written, but got logged off while writing so it is lost to the ages)