Craft as an API provider & authenticaton
It sounds like you're not necessarily interested in authenticating against Craft's current users, but you just want some type of header authentication in place.

If you set those header (via whatever means) in the API request, you can have a plugin's controller read those via HeaderHelper::getHelper($headerName) and perform whatever authentication logic that you require.

If authentication passes, let the request go through, if not, you can throw new HttpException(503);.