How to reassemble 3ds xl hinge?

If you've taken the hinge barrel completely out, how do you get it back in? I've only seen repair videos where it was never taken out.

My old one wouldn't line up to push all the way back in to put the hinge together but I have a new one that will slide in. The problem is that the white half moon is not lining up with the black half moon slot inside. Wiggling it around is not working. It's like I need to close the hinge FURTHER than possible to get them to line up. I can get the old one in now after using pliers to rotate the white plastic part (but it won't go any further) but it has the exact same problem now. How can I get them to line up??

(see how the half moon is off center? The black slot seems to be perfectly centered)