The LBS said that yeah, all you need to do is to loosen the screw marked in green in that one picture, and the aluminum blocked with the teeth should just fall out. I showed them it didn't, and they attacked it with screwdrivers, pliers, hammers, and brute force. After much banging of my bike on the floor, the thing popped loose.

So you guys were all right, the bike was just damn stubborn. Thanks for your help!