Dynamic scheduling of access to shared resources by autonomous systems is a challenging problem, characterized as being NP-hard. The complexity of this task leads to a combinatorial explosion of possibilities in highly dynamic systems where arriving requests must be continuously scheduled subject to strong safety and time constraints. An example of such a system is an unsignalized intersection, where automated vehicles' access to potential conflict zones must be dynamically scheduled. In this paper, we apply Neural Monte Carlo Tree Search (NMCTS) to the challenging task of scheduling platoons of vehicles crossing unsignalized intersections. Crucially, we introduce a transformation model that maps successive sequences of potentially conflicting road-space reservation requests from platoons of vehicles into a series of board-game-like problems and use NMCTS to search for solutions representing optimal road-space allocation schedules in the context of past allocations. To optimize search, we incorporate a prioritized re-sampling method with parallel NMCTS (PNMCTS) to improve the quality of training data. To optimize training, a curriculum learning strategy is used to train the agent to schedule progressively more complex boards culminating in overlapping boards that represent busy intersections. In a busy single four-way unsignalized intersection simulation, PNMCTS solved 95\% of unseen scenarios, reducing crossing time by 43\% in light and 52\% in heavy traffic versus first-in, first-out control. In a 3x3 multi-intersection network, the proposed method maintained free-flow in light traffic when all intersections are under control of PNMCTS and outperformed state-of-the-art RL-based traffic-light controllers in average travel time by 74.5\% and total throughput by 16\% in heavy traffic.