Disorganized thinking is a key diagnostic indicator of schizophrenia-spectrum disorders. Recently, clinical estimates of the severity of disorganized thinking have been shown to correlate with measures of how difficult speech transcripts would be for large language models (LLMs) to predict. However, LLMs' deployment challenges -- including privacy concerns, computational and financial costs, and lack of transparency of training data -- limit their clinical utility. We investigate whether smaller neural language models can serve as effective alternatives for detecting positive formal thought disorder, using the same sliding window based perplexity measurements that proved effective with larger models. Surprisingly, our results show that smaller models are more sensitive to linguistic differences associated with formal thought disorder than their larger counterparts. Detection capability declines beyond a certain model size and context length, challenging the common assumption of ``bigger is better'' for LLM-based applications. Our findings generalize across audio diaries and clinical interview speech samples from individuals with psychotic symptoms, suggesting a promising direction for developing efficient, cost-effective, and privacy-preserving screening tools that can be deployed in both clinical and naturalistic settings.