Two phase Indo-European movement

NYT:  In an article on the ancestry of Europeans based on new DNA findings:

Paul Heggarty, a linguist at the Max Planck Institute of Evolutionary Anthropology, said that the new studies were important, but were still too limited to settle the debate over the origins of Indo-European. “I don’t think we’re there yet,” he said.

Dr. Heggarty noted that the studies showed the arrival of Yamnaya in Central Europe about 4,500 years ago. But Greek is an Indo-European language, and the oldest evidence of writing in Europe shows that Greek had developed about 3,500 years ago. By then, it was distinct from other Indo-European languages in Southern Europe, like Latin.

If the Yamnaya were the source of Indo-European languages, they would have had to get to southern Europe soon after they made it to Central Europe.

Dr. Heggarty speculated instead that early European farmers, the second wave of immigrants, may have brought Indo-European to Europe from the Near East. Then, thousands of years later, the Yamnaya brought the language again to Central Europe.

This last has been my speculation, too, that the Harappan civilization was Indo-European, and then there was a second wave of Indo-European migration.   That would account for the Indian geography of the Rg Veda with less than 400 words with non-Indo-European roots in its 10,000+ word vocabulary; and the lack of non-Indo-European place names, the horse, etc.,etc.,etc.