The rapid development of Low Earth Orbit Position, Navigation, and Timing (LEO-PNT) constellations presents opportunities to augment Global Navigation Satellite Systems (GNSSs) with additional signals from Low Earth Orbit (LEO) satellites, thereby improving performance and reliability for users. This research study addresses the challenges posed by the interdependency between LEO and GNSS layers, which can lead to cascading faults. By extending Receiver Autonomous Integrity Monitoring (RAIM)-like capabilities to spaceborne receivers, specifically through Timing Receiver Autonomous Integrity Monitoring (T-RAIM), this paper aims to mitigate these risks. This study validates the integration of T-RAIM with advanced Precise Real-Time On-board Orbit Determination (P2OD) techniques in LEO scenarios using a hardware-in-the-loop test environment. The findings demonstrate that the architecture with T-RAIM can maintain nominal positioning and timing accuracy even in the presence of GNSS clock faults, ensuring continuous system functionality without requiring P2OD restarts. This capability is crucial to preventing service interruptions and enhancing the robustness of LEO-PNT solutions. The proposed integration handles the computational load and complexity while accommodating the limited resources of spaceborne receivers, offering a viable and robust LEO-PNT solution. The experimental results show that T-RAIM effectively mitigates the impact of pseudorange ramp errors, maintaining stable clock bias and preserving the integrity of orbit determination and time synchronization.