The anomalous gyromagnetic ratio (g-factor) of elementary particles---\textit{most famously the electron's deviation from the Dirac value}: gD = 2---has long been one of the most precisely measured and theoretically challenging quantities in fundamental theoretical physics. In Quantum Electrodynamics (QED), this anomaly is explained through radiative corrections represented by an infinite series of Feynman diagrams, culminating in the Dyson expansion. In the present work, building on the foundations laid in Paper (I), we develop an alternative, non-perturbative framework that traces the origin of the g-factor anomaly to the electromagnetic self-energy of an extended charge distribution coupled to a hypothetical cosmic vector field. By identifying the zeta-parameter [proposed in Paper (I)], which parameter governs the deviation from the Dirac value: gD = 2---with the spin-coupled electromagnetic self-energy, we derive a power series for the particle anomalous magnetic moments that reproduces the full Dyson expansion series of QED without invoking Feynman diagrams or perturbative methods. The coefficients of this series are shown to arise from the multipole moments of the charge distribution, as described by the Azimuthally Symmetric Theory of Electrostatics (ASTE-model) introduced herein. This framework naturally implies that particles with non-zero anomalous g-factors---including the electron---must possess a finite spatial extent. Using existing g-factor data for the proton, neutron, and lambda hyperon, we obtain a preliminary theoretical estimate of the electron radius: re = (1.20(5) e-22 m, in remarkable agreement with the stringent experimental upper limit: re < 1.50e22 m. We strongly believe that these results offer a fresh new perspective on the nature of fundamental particles, the origin of radiative corrections, and the possible existence of a cosmic field mediating spin-electromagnetic interactions across the fabric of spacetime.