Given the fact that schizophrenics seem to have different brain morphology, it seems that whatever causes it has organizational, not activational effects.

That is to say, the brain is permanently damaged during a critical period in a child's life, which leads to these effects later on. If it is a virus, perhaps it could be prevented, but almost certainly not cured.

Therapy to encourage new synapse development could also help, once any morphology-disrupting factor is removed.

That's because memories are built on those very synaptic connection you would need to rewire. Any cure that deals with reorganizing the brain could very well wipe out who they are. If it's even possible. And for that kind of technology we're talking at minimum centuries, not decades.