I don't think it's necessary to have a complete and deep understanding of Parshendi culture to predict this. He was able to foresee the reemergence of the Knights Radiant. This means he knows the voidbringers are coming back, and he also knows how. Even if he didn't know about the listener forms, how they worked, and their ability to call the Everstorm (despite him possessing a lot of lost knowledge about the desolations and the KR), he DID know the Parshendi would have a crucial role in it. He knew they would transform. He didn't even try to weaken the Parshendi at all. Their existence is known, their importance is know, their location is known.
A theory as to why he may need the Everstorm has to do with the cycle of Desolations and Odium. Potentially the desolation (termed the Final Desolation) needs to happen to defeat Odium once and for all.
Another theory is that a shard maybe influencing the Diagram. What Taravangian perceives as a fit of pure intelligence may actually have been influenced by a shard (maybe Cultivation, maybe Odium).