While most forks on platforms like GitHub are short-lived and used for social collaboration, a smaller but impactful subset evolve into long-lived forks, referred to here as variants, that maintain independent development trajectories. Integrating bug-fix patches across such divergent variants poses challenges due to structural drift, including refactorings that rename, relocate, or reorganize code elements and obscure semantic correspondence. This paper presents an empirical study of patch integration failures in 14 divergent pair of variants and introduces RePatch, a refactoring-aware integration system for Java repositories. RePatch extends the RefMerge framework, originally designed for symmetric merges, by supporting asymmetric patch transfer. RePatch inverts refactorings in both the source and target to realign the patch context, applies the patch, and replays the transformations to preserve the intent of the variant. In our evaluation of 478 bug-fix pull requests, Git cherry-pick fails in 64.4% of cases due to structural misalignments, while RePatch successfully integrates 52.8% of the previously failing patches. These results highlight the limitations of syntax-based tools and the need for semantic reasoning in variant-aware patch propagation.