Clarifying whether or not the Warring Triad plotline is part of the main story

[kuma_aus]

You need the optional EX primals done (except Thordan)

This is wrong. You need to do the quest that unlocks the quest to start the EX Primals. So you don't even need a Ravana EX or Bismark EX to start the Normal version of the fight. To start the EX version of the fight, you just need to clear the normal version. So once again you can never clear Bismark EX or Ravana EX and still clear the new EX.

But everything else said above sounds like the case.