Unlike the Hellenistic Greeks (ie, Questions of King Milinda), the Classical Greeks did not hold a high opinion of Indian wisdom. The impact of an occasional holy man cannot be discounted, but the total lack of any mention of Indians present in classical Greek sources is telling. Indians seem not to have passed the mouth of the Red Sea, and no embassies were recorded before Augustus. While gymnosophists receive much attention, it is their extraordinary ascetic and sensational acts (ie, Zarmaros' self-immolation) that receives attention, rather than the justification for those acts. Whatever Greek attention was paid to foreign religions was far removed from textual sources; even in the Hellenistic era, few Greeks appear to have read Egyptian, Zoroastrian, or Indian texts. Even if they did read them, the cultural gap between the Greeks and others would have been huge. Convergent evolution would seem a more likely reason for the Axial age, rather than direct influences.

Indian languages and religion have a clear external influence, but the evidence is murkier on population movements. The R1a1 marker doesn't look definitely Indo-European, as many Southern tribes (such as the Chenchu now looking for the lost chief of Andhra Pradesh) bear it. The caste studies you point to all compare Southern brahmins to other Southern caste populations; this may be simply be a north/south difference as many southern brahmin populations have northern ancestry, and their "non-Indian" ancestry is in line with reported figures from other northern populations. Nor can the admixture be isolated into Indo-European as opposed to, say, other numerous historically attested migrations into India (Jats, Rajputs, Bajara, etc.).  
 
Introduction of ideas outside the immediate environs of Greece seems highly unlikely given their xenophibia; though Zorastrianism quite possibly influenced Christianity.