The back of the monitor, from the top. The L hinges don't match up with the holes of the cabinet. The bottom of the monitor is basically fixed, since its screwed into the original bottom mount.
This is a closeup of the L hinge. I think this is the part that isn't right, but it looks like is should work. If you look at the bottom bracket and line up the top bracket, it seems like this is how it would have to mount. But the original cabinet holes suggest this isn't the method.
This is the original bottom bracket. From what I can tell, it has never been moved, so this should not be a variable that I need to change.