"For no other reason than" vs. "for no other reason that" vs. "for no other reason than that"
It seems to me that
For no other reason than
takes a nominal complement, and if what follows is a NP (eg your intransigence) it is simply used.
When the complement is a clause, it needs the complementiser "that", (eg that I want to)
Your number 2, on the face of it, makes no sense to me, but I would be quite prepared to believe that people say it for number 3.