Luckily they published their reasoning on the number of realisations in the supplementary materials of a prior paper cited in report 9 (citation 5): https://www.nature.com/articles/nature04795#MOESM28
"Numbers of realisations & computational resources: It is essential to undertake sufficient realisation to ensure ensemble behaviour of a stochastic is well characterised for any one set of parameter values. For our past work which examined extinction probabilities, this necessitates very large numbers of model realizations being generated. In the current work, only the timing of the initial introduction of virus into a country is potentially highly variable – once case incidence reaches a few hundred cases per day, dynamics are much closer to deterministic."
So looks like they did consider the issue, and the number of realisations needed is dependent on the variable of interest in the model. The code check appears to back their justification up, "Small variations (mostly under 5%) in the numbers were observed between Report 9 and our runs."