Humans display significant uncertainty when confronted with moral dilemmas, yet the extent of such uncertainty in machines and AI agents remains underexplored. Recent studies have confirmed the overly confident tendencies of machine-generated responses, particularly in large language models (LLMs). As these systems are increasingly embedded in ethical decision-making scenarios, it is important to understand their moral reasoning and the inherent uncertainties in building reliable AI systems. This work examines how uncertainty influences moral decisions in the classical trolley problem, analyzing responses from 32 open-source models and 9 distinct moral dimensions. We first find that variance in model confidence is greater across models than within moral dimensions, suggesting that moral uncertainty is predominantly shaped by model architecture and training method. To quantify uncertainty, we measure binary entropy as a linear combination of total entropy, conditional entropy, and mutual information. To examine its effects, we introduce stochasticity into models via "dropout" at inference time. Our findings show that our mechanism increases total entropy, mainly through a rise in mutual information, while conditional entropy remains largely unchanged. Moreover, this mechanism significantly improves human-LLM moral alignment, with correlations in mutual information and alignment score shifts. Our results highlight the potential to better align model-generated decisions and human preferences by deliberately modulating uncertainty and reducing LLMs' confidence in morally complex scenarios.