I don't know coding, but it seems like you could institute an "account tag" thing, where older users who have posted images that were not CSAM can post images without moderation, while newer users who don't have a track record are blocked from posting images (or links) until passed through moderation.
I imagine you could recruit volunteers to inspect those images and vote to pass onto mods if a grey area, or to block if obviously problematic. This would allow leaks or important cow-related news to be swiftly approved, while not inconveniencing new sign-ups with captchas or quizzes.
You would want to explain this on the sign-up page, obviously.
ETA: just saw a Null quote posted above, so maybe this wouldn't work.