If I’m understanding correctly, you would set in your pod which fact checkers had to be used to flag the information on the site as you see it? If so, I think that would be a great way to filter out some of the false flags.
I don’t know much about the Wayback machine, but as I understand it they have crawlers that crawl the web and archive web pages. Labels are added for different fact checkers and what they found. Then there is an API that you can call from an app to get archived web pages and you display the labels you choose and the related info. A crawl of the web can take more than a year, so it probably wouldn’t be practical to use your pod to make labels. But you could have something in your pod about which labels to display or not when the archived page is displayed, or you could ignore certain labels and call another fact checking service when the page is displayed, instead of when its crawled.