As is, given you’re pitching detecting resizing bugs, you should not have any on your sight that are not addressed; one thing not to acknowledge there’s content of functionality missing, another to not even acknowledge users are missing them by being on a given device.
All and all, I am surprised no one has coded an automated visual difference detection service for responsive. Thought about it in the past, but mainly for indexing websites, not doing QA on responsive templates.
Aside from the responsive aspect, you could also test the “reader mode”, no-JavaScript, etc for missing content.
As a sales “growth hack” — you could scan LinkedIn for people that would likely be a top contact for web QA/dev or marketing— and ping them to tell them you found a bug on the homepage and offer to QA there top 20 pages for free.