<p>The centripetal acceleration experienced by a maglev train traversing a vertical curve significantly affects both suspension stability and ride comfort. To improve the negotiation performance of high-speed maglev trains, this paper investigates the coupled vehicle–track dynamics and stability control under such conditions, incorporating control time-delay. The control parameter stability domain of the time-delay system is delineated based on the Hassard theorem, and compared with the delay-free case derived via the Hurwitz criterion. Results show that time-delay significantly compresses the stability domain, imposing a new upper stability limit on the velocity control parameters, which does not exist in the delay-free system. Theoretical and numerical analyses clarify that the upper stability boundaries for the displacement control parameters in both delayed and non-delayed systems correspond to the onset of Hopf bifurcation. Furthermore, the dynamic response of the system under track irregularity excitation is evaluated using the Monte Carlo method, revealing the inconsistency between the influence trends of control parameters on stability and ride comfort, and a corresponding parameter coordination strategy is proposed. Finally, a digital-twin predictive control framework is introduced to compensate for the adverse effects of time-delay on stability. Under ideal conditions, simulation results demonstrate that the proposed control method reduces the maximum nominal suspension gap deviation by 50.26%, while ride comfort is also improved with a 3.62% reduction in the maximum carriage acceleration.</p>