Is it possible that you keep looking at the problem wrong and it's not really a problem? I fail to understand how the cone is pushing anything out of place being that the cone has always locked the bearings in place as I tightened it. Are you using the right bearing size? I still don't understand why you are having so much trouble I think I could pack them with my eyes shut just by feel... Usually the grease holds it all in place right till when the bearing cone takes over. Unless you're not using enough bearings and leaving an unacceptable gap, but then that might explain why the manufacturer used caged bearings (other than simplicity of manufacturing of course.)
Even then a radial side groove bearing should mostly assemble itself in this kind of situation. Try working a little slower, might be you're trying to move too quick and it's messing up the method.