The topic of Co-creation, i.e., AI agents interacting with humans to generate outputs (e.g., art), has gained significant attention recently. However, most studies focus on adult-human interactions in a digital setting. This paper explores a novel ludic co-creation scenario involving children and Large Language Models (LLMs) interacting through a physical board game to create written stories. Our goal is to develop a multi-agent framework capable of producing high-quality narratives suitable for young players. At the core of our approach is an iterative Writer-Editor process in which one LLM generates stories while another evaluates them and provides feedback for refinement. Through a simulation study involving multiple LLMs, we show that this iterative interaction consistently improves the perceived quality of generated stories across successive loops. The results indicate that a small number of refinement steps may be sufficient to achieve high-quality outputs in interactive storytelling systems.