Thanks for the reply. I've got the layers separated by a bit, and I've tried larger and smaller amounts to resolve the issue to no avail. I've checked in on the B3D forums and was told the B3D/DX7 has a problem sorting alpha'd polygons. This is especially true when the objects are co-located...and all of my spheres share the same pivot as a parent object. Some of the jump routes have the same problem as they share the starting world's pivot.
I'm told the solution might be to shift the sphere centers progressively toward the camera a tiny bit, with the outermost being closest. This would have to be done dynamically, each time the camera moves...or at least moves a great deal. Sounds like a real pain in the behind, frankly, and I'll have to consider whether doing that work is more worthwhile than just rebuilding the thing in something like DBPro...or just C++ with OpenGL.
Who can say? In the meantime I've been working, slowly, on building a bit of a UI for the thing and lots of minor details. I hope to be largely done with it by this weekend, work and continuing sickness willing.