Hi Nelan,
When you are overlaying a component from the core component library, you will still need to "embed" the client libraries that are associated with each of the overlayed core components to get the CSS and JS working as expected.
To overwrite the CSS and JS, the standard way is to a new client library for your new overlayed component. Make sure the new client library embeds the core component's client library category(categories).
I hope this helps,
Brian