The current and upcoming generation of Very Large Volume Neutrino Telescopes - collecting unprecedented quantities of neutrino events - can be used to explore subtle effects in oscillation physics, such as (but not restricted to) the neutrino mass ordering. The sensitivity of an experiment to these effects can be estimated from Monte Carlo simulations. With the high number of events that will be collected, there is a trade-off between the computational expense of running such simulations and the inherent statistical uncertainty in the determined values. In such a scenario, it becomes impractical to produce and use adequately-sized sets of simulated events with traditional methods, such as Monte Carlo weighting. In this work we present a staged approach to the generation of expected distributions of observables in order to overcome these challenges. By combining multiple integration and smoothing techniques which address limited statistics from simulation it arrives at reliable analysis results using modest computational resources.