Even if you overlay the spherical harmonics on top of an actual sphere and get some of the same results mathematically, the geometry of the shell can't account for things like electron capture, which requires that electrons spend some time in the nuclear volume (unless we discard our understanding of the weak interaction). A spherical shell (i.e., the orbitsphere) does not intersect with the nucleus.
This -electron capture - is a different aspect, that certainly is not covered by Mills model. I would even state, that Mills has no model for the nucleus - just for the proton, that is, by no way a nucleus, it is a basic particle.
One of the crucial points of Mills model is the correct treatment of relativistic flux. His model also holds for the nuclear level(s), but needs one additional step to be successful.
I would discard all (-most all) standard model nuclear theories anyway...