I've been thinking about this issue and I really liked the posed question:
Could you come up with a system that takes into account the incentives of parties on both sides, and that prevents huge legal bills from being generated?
What if instead of immediately taking down the content, users were given 24 hours to respond that their content is non-infringing. If the users did not respond, it'll be taken down after 24hrs, but the user still has the ability to revoke the takedown notice. Or we can even make it so the content is taken down immediately, but allow the users to revoke the takedown notice and even provide a reason why their content is fair-use/non-infringing.
The problem today with takedown notices is that there's very little recourse for the user. The user "can" re-upload their content, but most likely will be flagged the next time around with these automated detection systems. I mean do we really need a counter-notice just to restore user content that is fair use?
With this model, I'm assuming people who know they're infringing will not respond or take down the content immediately (sort of like a cease/desist order). Only those who believe they're not infringing would bother responding to the notice. This would also help further narrow down the number of cases the other side has to verify. (e.g. YouTube will send back a list of content where users have responded to claiming it's fair use/non-infringing.)
Of course the media companies can still send an immediate take down notice for particular content they're sure are infringing, but for anything using automation to detect infringing content, the user should be given an option to respond before taking down, or a chance to easily restore the content.
If you're wondering what would deter an infringer from always responding back and saying it's non-infringing when it is? Banning the user and removing all his content could be a deterrent. Another possibility is the media company now has a legit case to actually sue the user for damages.
Just my 2 cents.