Motion planning among multiple robots in a shared space is a fundamental yet computationally challenging problem in robotics, with applications ranging from warehouse automation to autonomous fleets. In this work, we introduce a fast, scalable motion planner that achieves real-time, collision-free trajectory planning via a two-staged algorithm combining deterministic search-based planning with machine learning-driven conflict resolution. We present a prioritized Safe Interval Path Planning algorithm (SIPP-PP) with a novel limited goal reservation strategy to prevent goal-blocking conflicts while allowing shared goal regions. We added a second layer of ML-guided Large Neighborhood Search (LNS) procedure to our SIPP-PP algorithm for improving success rates in highly congested environments via intelligent selection of conflict resolution actions. The result is a planning system that generates collision-free paths for multiple robots in complex environments within tens of milliseconds. For example, compared to recent advanced learning-based methods such as diffusion planners, our planner is two-to-three orders of magnitude faster. Our work demonstrates a multi-robot planner capable of real-time operation in dense scenarios, satisfying the stringent requirements of industrial applications such as drive units in fulfillment centers.