Outline-conditioned story generation using Large Language Models (LLMs) offers a promising approach for automating narrative creation. Some outline-conditioned story generation methods use automatic scoring during the generation process in order to improve the story quality. However, current research has shown that automatic scoring is not ideal for assessing story quality. This paper evaluates three proposed automatic story-scoring methods to improve the reranking of outputs during the generation process. These scoring methods leverage different prompting strategies and fine-tuning techniques to enhance the accuracy and relevance of the assessments. By experimenting with these approaches within a beam search framework, we aim to identify the most effective methods for optimizing story-generation outcomes. While we have found no significant overall difference between these methods in terms of their agreement with human ratings during story generation, the overall story ratings by human evaluators are average. These findings motivate the need for improved automatic scoring techniques and datasets while also indicating that simpler, more easily implementable scoring methods for reranking perform comparably to more complex approaches.