Word-level cross-lingual alignment is central to annotation projection, translation auditing, and cross-lingual faithfulness estimation, yet existing neural aligners are rarely adapted to specialized domains. In this paper, we introduce ClinicalAligner26AM, a large-context multilingual aligner model for biomedical and clinical text initialized from ClinicalEncoder26AM. Our training recipe is inspired by AWESoME Align. We build our soft alignment target by sharpening with Sinkhorn-Knop optimal transport a cost matrix established for parallel clinical texts and conversations through the fusion of sentence-level, phrase-level, and token-level signals. We distill this sharpened alignment matrix directly into our student aligner, by encouraging its naive cosine-based token similarity scores to match this target. At inference time, we project source-span scores through the learned token alignment matrix and decode the longest valid high-scoring span in the target text, optionally supported by MultiClinNER predictions summarized in Appendix B. We evaluate CA26AM on the MultiClinCorpus shared task, which projects Spanish clinical entity annotations into six target languages. Our two submitted systems ranked respectively first and second across all languages and entity types, with character-weighted F1 scores above 0.95 in nearly all settings.