you are going to need to be very careful trying to get that edge to sit back down. it appears as though the top has fractured from the purfling ledge as well as split.
Forcing it back down may cause further fracturing if you can't get the binding to 'give' enough to set that exposed purfling back to where it should be.
I would think that the way to tackle this involves all sorts of stripping back, top removal and stabilisation and then re-setting it on the box and re-binding, if you can get the binding/purfling to move enough to get the top to sit down you might get away with wicking some thin CA into the fractures and splits and getting it all to hold together.
It's certainly going to be a tester. Is there anything rattling around inside it? DO you havee a mirror or one of those little scope cameras that you could use to check what that all looks like inside the box?