Large language models (LLMs) are increasingly being used in a zero-shot fashion to assess mental health conditions, yet we have limited knowledge on what factors affect their accuracy. In this study, we utilize a clinical dataset of natural language narratives and self-reported PTSD severity scores from 1,437 individuals to comprehensively evaluate the performance of 11 state-of-the-art LLMs. To understand the factors affecting accuracy, we systematically varied (i) contextual knowledge like subscale definitions, distribution summary, and interview questions, and (ii) modeling strategies including zero-shot vs few shot, amount of reasoning effort, model sizes, structured subscales vs direct scalar prediction, output rescaling and nine ensemble methods. Our findings indicate that (a) LLMs are most accurate when provided with detailed construct definitions and context of the narrative; (b) increased reasoning effort leads to better estimation accuracy; (c) performance of open-weight models (Llama, Deepseek), plateau beyond 70B parameters while closed-weight (o3-mini, gpt-5) models improve with newer generations; and (d) best performance is achieved when ensembling a supervised model with the zero-shot LLMs. Taken together, the results suggest choice of contextual knowledge and modeling strategies is important for deploying LLMs to accurately assess mental health.