Contemporary NLP has rapidly progressed from feature-based classification to fine-tuning and prompt-based techniques leveraging large language models. Many of these techniques remain understudied in the context of real-world, clinically enriched spontaneous dialogue. We fill this gap by systematically testing the efficacy and overall performance of a wide variety of NLP techniques ranging from feature-based to in-context learning on transcribed speech collected from patients with bipolar disorder, schizophrenia, and healthy controls taking a focused, clinically-validated language test. We observe impressive utility of a range of feature-based and language modeling techniques, finding that these approaches may provide a plethora of information capable of upholding clinical truths about these subjects. Building upon this, we establish pathways for future research directions in automated detection and understanding of psychiatric conditions.