You need a different approach. One that assaults the very foundation of Plato's outdated and state policy centric view: The soul and the analogy of soul and state. This is what his whole rhetoric is aiming at. The ideal state based on the big necessary truth. If the soul is not contingent, so the ideal state is not contingent. Show that the soul is contingent and his whole pov will vaporize. There are approaches around, you won't have to re-invent this wheel. Nominalists offer a good approach to refute Plato's absurd idea of forms. That is the essence, eternal, absolute, unchangeable ideas. Forms as supposedly abstract objects do not exist in the same sort of space and time that we ourselves do. So how can we have knowledge of them? Without knowledge of the idea of a soul how can the ontoöogigal state of something like a soul anything other than contingent? How can any knowledge we have be a memory of something outside the realm of our own space-time which is not necessarily existent? This would be my approach. It's far from sound in this brief answer I type on my cellphone but I guess you get the idea.