I added a few more details to my previous post.
Well, most Indo-Iranian people had certain differences among them. Even Pashtuns are different from the Baloch in many ways in spite of the fact that they are Indo-Iranian people. Cultures evolve separately, the Koshur language for instance is most similar to Rigvedic Sanskrit as far as I know. This also implies that when the age of Classical Sanskrit began at the time Panini came up with the grammatical rules for Sanskrit, it's influence over the Indo-Aryan people residing in Kashmir was minimal though they were naturally aware of it. To some extent, Kashmir was also isolated as the Vedic civilization was broken in to multiple kingdoms. Southern India & Bangladesh don't have anything if much to do with the Indo-Iranian migrations. There may have been some mixture with the local people, but that happens everywhere as people migrate from one land to another. Most of the Sub-Continent was culturally dominated by the Indo-Iranians & that is how their languages spread. The Indo-Iranian migrations & settlements remained in the north western & to some extent northern regions of the Sub-Continent. By the way, many Kashmiris do resemble Iranic ethnic groups.
Which origin myths? Are you referring to the ones here?
What time frame are you referring to when these migrations took place. Time frame is of utmost importance in order to contextualize the historical value of these migrations.