The availability of massive vehicle trajectory data enables the modeling of road-network constrained movement as travel-cost distributions rather than just single-valued costs, thereby capturing the inherent uncertainty of movement and enabling improved routing quality. Thus, stochastic routing has been studied extensively in the edge-centric model, where such costs are assigned to the edges in a graph representation of a road network. However, as this model still disregards important information in trajectories and fails to capture dependencies among cost distributions, a path-centric model, where costs are assigned to paths, has been proposed that captures dependencies better and provides an improved foundation for routing. Unfortunately, when applied in this model, existing routing algorithms are inefficient due to two shortcomings that we eliminate. First, when exploring candidate paths, existing algorithms only consider the costs of candidate paths from the source to intermediate vertices, while disregarding the costs of travel from the intermediate vertices to the destination, causing many non-competitive paths to be explored. We propose two heuristics for estimating the cost from an intermediate vertex to the destination, thus improving routing efficiency. Second, the edge-centric model relies on stochastic dominance-based pruning to improve efficiency. This pruning assumes that costs are independent and is therefore inapplicable in the path-centric model that takes dependencies into account. We introduce a notion of virtual path that effectively enables stochastic dominance-based pruning in the path-based model, thus further improving efficiency. Empirical studies using two real-world trajectory sets offer insight into the properties of the proposed solution, indicating that it enables efficient stochastic routing in the path-centric model.