If your work is already published recently, then you can still apply for copyright registration. The deposit requirement changes for physical published books. You need to deposit a physical copy if it is already published in physical format. Therefore, you still have a priority. Copyright ownership has nothing to do with the registration. The two-year filing requirement is applicable for mask works and vessel designs. For statutory damages purposes, just file a copyright registration for the published work.
Answered on Dec 15th, 2019 at 2:19 PM