Just implement the system, as in most of the rest of the civilized world, where it assumes - in all probability - that one party in a law suit is not behaving in good faith. And that person should pay the cost.
So, in this particular case, if you send a takedown notice I reply with a put-back. If you decide to take it further, and I win, you end up paying me my solicitors costs, my losses while my stuff is down, etc etc. Basically, you have to make me whole for your false accusations.
And if it's your automated system making the mistakes, it's rather expensive to pay real people to put it right :-)
It'll only take a few people starting to fight back, and the game will very quickly cease to be worth the candle for the MAFIAA.