Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using probabilistic models of future demand. However, computational cost can become a severe challenge when evaluating large probabilistic electricity demand forecasting models with long forecasting horizons. In this paper, Monte Carlo methods are developed to increase the computational efficiency of obtaining asset overload probabilities from a bottom-up stochastic demand model. Cross-entropy optimised importance sampling is contrasted with conventional Monte Carlo sampling. Benchmark results of the proposed methods suggest that the importance sampling-based methods introduced in this work are suitable for estimating rare overload probabilities for assets with a small number of customers.