Nice try, but the superposition of perturbed spheres is still sphere, not the fancy orbital shapes like these ones. These shapes just determine the angles of chemical bonds by geometry of resonating quantum waves, not additional calculations based on experimental values.
Where did you read that QM needs no gauge?? Are you just guessing the mass of a nucleus?? And who is measuring the base (Bor equivalent) radius? The fact is that not even for Hydrogen the exact charge radius is known, because QM is no help in that case.. and many others. (Look at the QM calc for the elctron g-factor - way off!)
Mills calculation just delivers the force relevant orbits for the static calculation of basic atom/molecule features nothing more. Mills would never deny the existence of an electron cloud, but for his calculations it is not important.
Enviousness is never a guide to success, just think about it.
(PS: Only the superposition of non perturbed spheres are still spheres! Just think of the overlay of rotation torque and bending torque vibrations! Even a simple molecule like H20 has two free degrees for torque vibrations!)