My findings is that it is not possible to add singletons after the game started and running.
I solved that like this:
1, create placeholder/dummy singletons manually in editor before the game started.
2, Import the resources/scriptis with ProjectSettings.loadresourcepack(...) in runtime.
3, replace all singletons's script with set_script(...) in runtime.
This requires planning. Singleton names and paths must match.