Qualitative coding is central to social science, but expert annotation is difficult to scale. LLMs offer a possible extension, yet require careful validation when the target construct is interpretive, theoretically loaded, and only indirectly expressed. We study this problem in a difficult case: detecting whether authors treat Bayesian models as descriptions of mental and neural mechanisms (realism) or as useful mathematical tools (instrumentalism). Our method combines a theory-driven codebook, expert-coded reference annotations, a diagnostic-gated prompt-optimization search yielding a shared zero-shot prompt for three frontier LLMs (GPT-5.1, Claude Sonnet 4.6, Gemini 3 Pro Preview), and multi-rater reliability analysis. The final prompt achieved a held-out combined reliability score of 0.76 (harmonic mean of ICC = 0.79 and
α = 0.74), with all diagnostics satisfied. Deployed on 6,858 quotes from 210 articles, the three LLMs reached substantial quote-level agreement (ICC = 0.80;
α = 0.76; combined = 0.78) and near-perfect article-level rank stability (
r = 0.96-0.97 across rater pairs). The corpus was predominantly weakly realist, but article-level stances were rarely uniform: only 1.4% of articles used a single band, while 59.5% spanned four or more. Low-level perception/motor articles scored 8.8 Realism points higher than high-level cognition articles (
p<.001,
d=0.60), quantifying a long-held qualitative intuition. We present this as an expert-led case study; the framework is intended to generalize to similar theoretically demanding tasks, not to all qualitative analysis.