The generation and sustainment of stable, high-field Spheromak configurations remain critically limited by global tearing and tilt instabilities during helicity injection. This paper presents a novel theoretical and mathematical framework, which resolves this limitation by treating forced magnetic reconnection as an actively controlled Hamiltonian chaos system. We demonstrate that by applying High-Frequency Adaptive Stochastic Resonance (HFASR) - specifically, launching localized shear Alfvén waves tuned to the macroscopic magnetic shear length (L) - we can surgically induce micro-scale stochasticity at targeted rational q-surfaces. Using a phenomenological systems-dynamic framework coupling macroscopic scaling laws with the Klein-Kramers formalism, we theoretically demonstrate that this localized tearing acts as a 'stochastic pump.' The resulting energy released from destroyed Kolmogorov-Arnold-Moser (KAM) surfaces initiates a robust inverse turbulence cascade. Most crucially, we establish the existence of a "Phase-Locked Attractor" in the system's phase space. Provided the external radio-frequency (RF) modulation is phase-locked to the plasma's local Kramers transition rate (rk), the chaotic eddies self-organize, continuously transferring magnetic helicity to the global Taylor state (ψ0). Dynamic Grad-Shafranov simulations demonstrate that this mechanism successfully amplifies a 3 T Coaxial Helicity Injection (CHI) seed to a stable > 12 T core field without exceeding the Chirikov threshold for global stochasticity (S < 1.0). This validates the proposed framework as a viable pathway for maintaining impenetrable, nested KAM surfaces during rapid, non-equilibrium field amplification, opening the door for compact, high-field aneutronic fusion topologies.