Spin–orbit torque MRAM (SOT-MRAM) is a leading candidate for next-generation nonvolatile memory, offering high speed, endurance, and architectural compatibility. However, in conventional SOT switching, the magnetization remains near the in-plane region at pulse termination, making the final state highly sensitive to post-pulse relaxation dynamics and prone to back-switching. To overcome this, we propose a field-free scheme in which the transverse SOT drives large-angle precessional excitation while the perpendicular spin-transfer torque (STT) biases the trajectory toward the reversed -z state. Micromagnetic simulations reveal a nonlinear switching boundary in the J_STT--J_SOT parameter space, originating from the distinct dynamical roles of the two torques: SOT primarily governs the excitation and crossing of the dynamical separatrix, whereas STT controls the terminal trajectory and final-state selection. An analytical macrospin model, based on the stability analysis of the current-induced equilibrium, reproduces the critical-boundary trends as functions of current density, Gilbert damping α, and uniaxial anisotropy Ku, and distinguishes dynamic anti-damping and static instability branches. Systematic analyses of pulse duration, damping, anisotropy, and the STT–SOT balance further demonstrate that reliable ultrafast switching requires not only sufficient excitation to cross the separatrix before pulse termination, but also precise control of the pulse-end magnetization state to minimize post-pulse relaxation. These results establish that the pulse-end state, rather than the instantaneous torque amplitude, is the decisive factor governing switching speed and reliability in coupled STT–SOT systems.