I will go to Iran without CPD next year. I will go to Georgia and Armenia and next transit to Turkey.
Few days ago I red about Polish travelers stopped in Bazagran border without CPD. They spent 20 hours (most of it sleeping) on border and went to Iran by transit to Armenia. Border officer said that they can stay in Iran 20 days without any problems.
So it is possible and even more pleasant than buying CPD
I think only what will be better: Turkey-Iran-Armenia or Armenia-Iran-Turkey???