I don't see the addon anymore in my list; that likely means it was a casualty of when Firefox changed its addon infrastructure around a few years back. Some brief Googling seems to indicate it might have been "CacheViewer", though I can't check as it's "incompatible" now. Oh well.

Really, you need something that lets you sort the cache entries by the URL (so you can easily highlight all of the FKG ones in one go), and then some download/export/save as option to dump all of those selected files somewhere. That's the tricky part. The "clean cache at the start" should be doable from any normal browser, without bothering with addons.