The scheduling of quay cranes is a core logistics challenge that affects significantly the loading and unloading time of a vessel berthed at a container terminal. In this paper, we study the Stochastic Floating Quay Crane Scheduling Problem involving cranes situated on the quay of an offshore modular platform. Specifically, we consider the case in which each crane is situated on a different module of the platform, thereby confining its operation range. Additionally, we assume stochastic crane productivity rates due to the effect of the offshore wind. To tackle the problem, we propose a simheuristic framework, which combines Iterated Local Search with Monte Carlo Sampling into a joint collaborative scheme. The main objective is to minimize the expected completion time of the loading and unloading process taking into account precedence, nonsimultaneity, non-crossing, and spatial constraints of the problem at hand. The performance of the proposed simheuristic is investigated on a set of established problem instances across different configuration parameters and under various real-world environmental scenarios offering insightful conclusions.