I’ve got an update. I attempted to re-add the removed module and now UE4 reports that it’s missing two modules:
UE4Editor-[GameName].dll and
UE4Editor-[GameName]Editor.dll
I guess I was mistaken in assuming that the missing .dll was the removed module, it appears to have been the actual game’s .dll. How can I go about recompiling it seeing as UE4 can’t do so automatically?