:;()$&@"\The Anime Pub/:;()$&@"

I'm of the opinion that there is only one world line. While it does switch "locations" (for a lack of a better word) from time to time as we have seen, it's the only one existing. As of now there's no way of proving the opposite, the only way to do that would be observing a different world line without interfering with the current one, which thus far hasn't happened. The only times Okabe observed different events in the world line, it was when he was inside it. As you said, everything else is nothing but a possibility, sometimes one that has been realised, sometimes it wasn't. Ones that have been tried are ones that can still faintly linger in the memories of other people if they had enough of an impact to burn themselves deep into the subconscious and this did not get completely erased. Which might explain why they almost exclusively appear in dreams.
That means, we can assume that Okabe is (again something you already said) an almost godlike observer entity and likely the only currently living being that has any way of interfering with different possibilities of the world line. Which means that the fate of humanity is decided by whether or not he becomes insane. And the only reason he hasn't thus far is Mayuri in my opinion. I don't know if she knows for certain or just has a hunch or something, but she appears to somehow know that the dreams she had about her own deaths were more than just dreams. Also, she's always somewhere close to Okabe in zero whenever he's together with a lot of other people (excluding university). The few times we see the two of them seperated AND something triggering one of his suppressed memories, he gets very close to a mental breakdown. At the very least, Mayuri knows that she is somehow connected to his suffering and she always tries her best to cheer him up. Without it, I think he would've lost his mind long ago.
Then again, I could be reading too much into things. After all, it's not like I know a whole lot about traumata and psychology in general. Still, I think it makes at least some sense.