We propose a neutrino detection architecture based on dense cesium halide crystals operated near a structural phase instability and driven into a nonlinear Floquet-stabilized metastable regime. Instead of attempting to enhance weak-interaction cross sections, the approach exploits coherent elastic neutrino--nucleus scattering (CE$\nu$NS) at solid-state densities ($\sim10^{22}$ cm$^{-3}$)~\cite{freedman1974,scholberg2006} and amplifies the resulting $\sim$10 $\mu$eV nuclear recoil via proximity to a dynamical bifurcation. We analyze recoil energy scales, phonon displacement amplitudes, structural barrier energies near soft-mode transitions, thermal constraints, and the conditions required for deterministic attractor switching. The analysis indicates that operation below $\sim$20 mK and near a saddle-node Floquet instability may allow a 10 $\mu$eV localized recoil to induce a measurable, persistent change in the driven system's dynamical regime (observed via the order parameter $M_s$) in an engineered cesium halide lattice. The proposal reframes neutrino detection as a nonequilibrium phase-space instability problem rather than a purely calorimetric one. Source code for c++/python in zip file.