Something like an Perso-Afghan Pakistan and an Indian Pakistan, with only Islam connecting the two as a nation state?
Can we then say that the conflict within Pakistan stems more from a clash of people and bloodlines and less from religious differences per se, as a significant half of Pakistan seems disconnected from the Indian half and sees themselves as essentially different?
In effect, a sociocultural buffer zone between the ancient Persian and Indian civilizations?
Possible, but currently one identity is winning over the other due to being more organized and that would be the Perso_afghan Pakistan.. It has due to its cultural similarities with the Arabs "trademarked" Islam in Pakistan and uses this to exert influence over the other side. And while the Disconnect is not as such , the dis-balance of influence on Islam in Pakistan is.
There are also many cultural activities in Pakistan that have nothing to do with Islam and go against it , yet are carried out on the shrines of sufi saints..such activities are culturally descendant from the people and their pre-Islamic heritage and earn the ire of many Pakistani Muslims.
Again, without a centres that guide Islamic thought in Pakistan..such issues will only grow.
Moreover.. apart from Islam there are other identity forces at play based on the age old sub-continent issue of caste and creed.
And the two cultural sides you have defined(loosly) are usually at angst over each others assumed "pride" in their heritage.