We present a covariant scalar-tensor extension of General Relativity where a scalar field $\phi$ selectively couples to the mixed spacetime components of curvature via $R_{0i}R^{0i}$. The theory is derived from a variational principle with a logarithmic potential, ensuring exact recovery of General Relativity for all stationary spacetimes. Gravitational waves retain two tensorial polarizations and propagate at light speed in weak fields. Observable deviations emerge only during highly dynamical events like binary black hole mergers, predicting modified ringdown structures, enhanced overtones, and gravitational birefringence. The framework is ghost-free, tachyon-free, and energy-momentum conserving, providing a testable hypothesis for extreme gravity with current and future gravitational-wave detectors.