Millimeter-wave (mmWave) multi-user MIMO systems are highly vulnerable to blockage, and reconfigurable intelligent surfaces (RIS) have been proposed as a remedy. However, RIS links may themselves be blocked, while most prior works assume ideal RIS availability. We propose an end-to-end blockage-aware multi-RIS weighted sum-rate (WSR) optimization framework. The BS transmits short per-RIS indexed synchronization signals, enabling each user to identify blocked panels through a simple energy detection test. Based on the detected feasible sets, we jointly optimize the BS precoder and RIS phases via a Closed-form Riemannian Phase Alignment (CRPA) algorithm. CRPA provides unit-modulus-preserving closed-form updates, requiring no projection or line search, and ensures monotone ascent. Simulations validate reliable blockage detection and notable WSR and convergence gains over existing baselines.