To what extent can LLMs be used as part of a cognitive model of language generation? In this paper, we approach this question by exploring a neuro-symbolic implementation of an algorithmic cognitive model of referential expression generation by Dale & Reiter (1995). The symbolic task analysis implements the generation as an iterative procedure that scaffolds symbolic and gpt-3.5-turbo-based modules. We compare this implementation to an ablated model and a one-shot LLM-only baseline on the A3DS dataset (Tsvilodub & Franke, 2023). We find that our hybrid approach is cognitively plausible and performs well in complex contexts, while allowing for more open-ended modeling of language generation in a larger domain.