> I just ran a backup, and it was 850MB. So having my phone upload something of that size every day would be a bit annoying
It may be inconvenient but this can be solved by using the features in the app to review your storage and save those thousands of images/audio/file sequestered inside the app out to the filesystem, then delete them from the app. You're not backing up "chats" you're backing up your image library being stored inside a chat app.
(yes I get the argument that you need to store them "in context" so save those and do the rest. there's no way 100% of that 850MB is "must have saved inside the app in chats" data, I'll bet $10 USD on it)