I think the Occurrians canīt fight humans physically.They can only possess people who makes wrong decisions.That is why they canīt protect the sun cryst.
I donīt understand how people missed the fact that the background of the labyrinth on the middle of Giruvegan is exactly the same that we see on the Bahamut wirlwind on the beggining of the scene where we enter the final dungeon(the war between Bahamut and Bujerba).
And understand thiseified Nethicite didnīt exist.All of these special shards comes from the sun cryst which is nothing more than manufactured nethicited haunted by the Occurria .Canīt you see what is the pharos on the past?Try to guess(66 is the first floor number that we see on the pharos and the lowest we see on some other place.This canīt be a coincidence).The Occurria is obviously lying if they are conspiring.Duh.
Cid donīt go magically to the past.He does it through space and ends there because they joined the eras spacially(some sort of magic).Cid doesnīt even know about the time travel.
Read my simplified explanation of the time loop,please.And time travel is hinted countless on the names of the maps.