My plugin Master can help! It can automatically find and attach all instances of the original component to the new library component and preserve all overrides. Here are the full instructions on how to do it, below is a shortened version:
Copy the main component you want to move to the library and publish it.
Select this new library component and run: Plugins → Master → Pick Target Component.
Select the original component or its instances and run: Plugins → Master → Link Objects to Target Component.
If that component was local, that’s it. If not, you need to go to each file where instances of it are used, deselect everything and run Link Objects to Target Component.
A new video showing how to move components with Master: