I actually spent a few years of my life writing a whole software project for exactly this purpose, and I still think that it's the only practical way to solve this problem.
Called "Aletheia", it ditches the idea that software can spot a fake entirely and instead provides a way to guarantee the author of a piece of media. If you trust the source, you can trust the image/video/document/whatever.
If you're curious, here are a few relevant links: