Running up stairs is effortless for humans but remains extremely challenging for humanoid robots due to the simultaneous requirements of high agility and strict stability. Model-free reinforcement learning (RL) can generate dynamic locomotion, yet implicit stability rewards and heavy reliance on task-specific reward shaping tend to result in unsafe behaviors, especially on stairs; conversely, model-based foothold planners encode contact feasibility and stability structure, but enforcing their hard constraints often induces conservative motion that limits speed. We present FastStair, a planner-guided, multi-stage learning framework that reconciles these complementary strengths to achieve fast and stable stair ascent. FastStair integrates a parallel model-based foothold planner into the RL training loop to bias exploration toward dynamically feasible contacts and to pretrain a safety-focused base policy. To mitigate planner-induced conservatism and the discrepancy between low- and high-speed action distributions, the base policy was fine-tuned into speed-specialized experts and then integrated via Low-Rank Adaptation (LoRA) to enable smooth operation across the full commanded-speed range. We deploy the resulting controller on the Oli humanoid robot, achieving stable stair ascent at commanded speeds up to 1.65 m/s and traversing a 33-step spiral staircase (17 cm rise per step) in 12 s, demonstrating robust high-speed performance on long staircases. Notably, the proposed approach served as the champion solution in the Canton Tower Robot Run Up Competition.