I present a disorder-free, two-dimensional Floquet stabilization mechanism that maintains a clean periodic orbit for more than 5000 cycles on a $30times30$ square lattice. The drive consists of a global transverse field and a purely imaginary nearest-neighbor interaction with a slow spiral phase profile of maximum amplitude $pi/512$. Mean-field product-state simulations (size $1800$, fourth-order Runge--Kutta, 200 steps per period) show that this imaginary phase twist passively suppresses Floquet heating for thousands of periods without disorder, feedback, or long-range couplings. A hardware test on a $3times3$ patch of an IBM superconducting device (50 periods, approximately $10^6$ physical gates) produced no detectable subharmonic response, consistent with the expected sensitivity of the mechanism to global coherence and the destructive effect of individual addressing. To verify that the stabilized orbit encodes an effective logical manifold, I applied a global logical-$X$ operation across three qualitatively distinct initial states (polarized, N'eel, and random). In all cases the sign of the logical magnetization $Z_L$ inverts while the magnitude remains small ($sim 10^{-3}$), indicating that the operation acts as a symmetry of the Floquet orbit rather than a state-preparation artifact. The resulting drive maps directly to a single global radio-frequency field plus a static magnetic-field gradient on current two-dimensional trapped-ion platforms, suggesting a route toward robust low-frequency logical qubits and potential applications in isotope- or chirality-selective sensing.