Secure patient-provider messages contain clinically important communication behaviors that are difficult to characterize manually at scale. The Electronic Patient-Provider Communication (EPPC) framework provides an ontology for coding these behaviors, but automated extraction remains challenging because predictions must preserve fine-grained code/sub-code structure while grounding annotations in message text. We developed EPPC-OASIS, an ontology-aware adaptation approach for structured EPPC extraction, and combined it with deployable inference-refinement procedures designed to improve the coherence of final annotations. EPPC-OASIS augments supervised fine-tuning with a Wasserstein alignment objective that encourages alignment between model representation neighborhoods and EPPC ontology-derived neighborhoods, while inference refinement uses verification, self-consistency, hybrid correction, and selection or ensembling to address residual prediction errors. We evaluated the framework on a de-identified corpus of secure patient-provider messages against prompting, supervised fine-tuning, preference-based, and robustness-oriented baselines across multiple open-weight language models. Across model families, the best deployable pipeline achieved 77.13% Code+Sub-code F1 and 63.83% Triplet F1, corresponding to modest but consistent absolute gains of +1.39 and +2.12 F1 points over the strongest supervised fine-tuning baseline. These results suggest that ontology-aware adaptation with structured inference refinement can support scalable retrospective EPPC mining, although external validation is needed before operational use.