What are the best options for performing Web Scraping of a not currently open tab from within a Google Chrome Extension with JavaScript and whatever more te
I think you can start from this example.
So basically you can try using Extension + Plugin combination. Extension would have access to DOM (including plugin) and drive the process. And Plugin would send actual HTTP requests.
I can recommend using Firebreath as a crossplatform Chrome/Firefox plugin platform, in particular take a look at this example: Firebreath - Making+HTTP+Requests+with+SimpleStreamsHelper