I was able to somewhat resolve this problem, although I would think there should have been an easier solution…
I made a new, blank and clean 5.6 project. Migrated over all project files from the original project into the new one. I enabled all my necessary plugins and project settings (nothing changed). Once I was complete with migration, I packaged the project as usual (Windows/x64), and it worked.
I tried everything I could think of with the original project, but nothing worked. The hash values for the animations were corrupted somehow during the 5.5 → 5.6 project update.
~8 hours lost trying to find a solution, when in the end the only option was nuclear… oh well.