Systematic reviews and meta-analyses rely on converting narrative articles into structured, numerically grounded study records. Despite rapid advances in large language models (LLMs), it remains unclear whether they can meet the structural requirements of this process, which hinge on preserving roles, methods, and effect-size attribution across documents rather than on recognizing isolated entities. We propose a structural, diagnostic framework that evaluates LLM-based evidence extraction as a progression of schema-constrained queries with increasing relational and numerical complexity, enabling precise identification of failure points beyond atom-level extraction. Using a manually curated corpus spanning five scientific domains, together with a unified query suite and evaluation protocol, we evaluate two state-of-the-art LLMs under both per-document and long-context, multi-document input regimes. Across domains and models, performance remains moderate for single-property queries but degrades sharply once tasks require stable binding between variables, roles, statistical methods, and effect sizes. Full meta-analytic association tuples are extracted with near-zero reliability, and long-context inputs further exacerbate these failures. Downstream aggregation amplifies even minor upstream errors, rendering corpus-level statistics unreliable. Our analysis shows that these limitations stem not from entity recognition errors, but from systematic structural breakdowns, including role reversals, cross-analysis binding drift, instance compression in dense result sections, and numeric misattribution, indicating that current LLMs lack the structural fidelity, relational binding, and numerical grounding required for automated meta-analysis. The code and data are publicly available at GitHub (https://github.com/zhiyintan/LLM-Meta-Analysis).