You didn't say what type of glue you used. If it's TB then you don't want to use a crazy glue to try and repair it, the two don't get along very well. I find crazy glue to be a bit too brittle anyway.
In any case this is what I would do, and this has worked for me in the past. Get a slow setting, good quality epoxy that is not bothered by oily woods. Mix up a small quantity and pry the backing apart like you are doing in the picture. Heat the backing up till it's hot, not too hot that you can't keep your hand on it though. Then apply the epoxy to the crack, the heat will turn it to the consistency of water and you'll see it run into the crack. Apply as much as needed till it won't absorb any more. Then use a padded clamp and clamp the split down and release it, you'll see air bubbles come out as you clamp it. This is to make sure there's no voids inside. After you've done that a few times apply a bit more glue, just to make sure, and clamp it down and let the glue set.