You should be able to use a clear-dry waterproof glue, if you have a bit of time to work on it.
What I would do is coat each surface in turn with the glue, and also have a rag ready with some glue solvent on it. (Test the solvent ahead of time to make sure that it won't damage the rhinestones.) Paint the glue on so that it goes down into the crevices between the stone, wait just a while until it is tacky but not fully set, then use the solvent to polish the surfaces of the stones so that the glue is removed from that area but not from the crevices between. Prop up the case for several hours so that the surface you treated dries completely and is fully set, then turn it and do another surface, etc.
It will probably take two days to do the entire thing without leaving any of the stone's surfaces coated with glue.