Aspect-category sentiment analysis provides granular insights by identifying specific themes within product reviews that are associated with particular opinions. Supervised learning approaches dominate the field. However, data is scarce and expensive to annotate for new domains. We argue that leveraging large language models in a zero-shot setting is beneficial where the time and resources required for dataset annotation are limited. Furthermore, annotation bias may lead to strong results using supervised methods but transfer poorly to new domains in contexts that lack annotations and demand reproducibility. In our work, we propose novel techniques that combine multiple chain-of-thought agents by leveraging large language models' token-level uncertainty scores. We experiment with the 3B and 70B+ parameter size variants of Llama and Qwen models, demonstrating how these approaches can fulfil practical needs and opening a discussion on how to gauge accuracy in label-scarce conditions.