The split is indeed very interesting & the mirror symmetry is very intriguing. I have wondered at it quite a bit over the years.
I do not think that the Prophet Zartosht (Zoroaster) (AS) adopted the shared roots, rather he pruned the proverbial collective burning bush of the Aryaman tribes.
His revelations, at least in form handed down to us, are in part very confident Q & A sessions with God, his "Friend", and to an extent include theological matter dismissing certain notions, practices, and spiritual agencies. One gathers that there was a sort of free for all in terms of appeal to higher agencies at his time, in the shared millieu of the region.
Note that there is a small hop from Persian Deev to Devil to counter balance the Deva to Divine. Zartosht's message was nothing if this: not all powers are pure (holy) and there is a Cosmic Choice to be made, and that this choice has eternal consequences. According to him, the Good is fundamentally Creative and Truthful. The evil is a destroyer and a liar. (Direct analog of which you can find in the Gospels.)
Accepting that, one can then easily map the Zoroastrian informative doctrine of 'Good thought, Good Speech, Good Action' to related Indian scripture (e.g. The Gita) and discourses on Karmic causality.