A question, invaders or not, there have been East Asians invade and conquer India for vast stretches of time. Have their haplogroups simply disappeared, or have the Indians eliminated their offspring, or expelled them (as they expelled Buddha's family in the Hindu Revival).
Or, are we dealing with some other biological function that inhibits the reproduction of some haplogroups at that latitude.
All anthropological evidence from pre history supports the fact that most of the push of mass human migration was from West (Asia) to East. Not the other way....unless you are talking about Mongol invasion which happened only a few hundred years ago. Other then that I dont know what East Asians you are referring to who “invade and conquer India for vast stretches of time”. By the way there was never a direct Mongol invasion of India until Babar who was half Mongol. The closest would be the Khmers who ruled Cambodia who were actually Austro-Asiatic from eastern Indian. The Austro-Asiatic still exists among the Munda tribe who have language that is a close match to the Khmer but thats a case of Indian tribals populating Indo-China.
As for your commentary on Buddha's family being expelled. I dont know where you got that from. Seems to me you have mixed up a lot of myths and mumbo jumbo ideas into your constructs.