On the contrary, the largest parts of Anatolia
were IE speaking. They were also not the parts anywhere near the Balkans. You people just ignore everything that doesn't fit on your side of the ledger. There's nothing scholarly about your approach whatsoever.
Why focus only on the Hittites?
I'm sorry, but only people with an agenda are going to believe this if not one sample in this whole area shows EHG. There's still time for the samples to show up, of course, but as I said, if none show up it's a real problem.
As for the mummies, come on. If you want Egyptian mummies with some "Greek" ancestry in them this is not the place to look. Look in Alexandria, for goodness' sakes. That's where the vast majority of the Greek citizens lived. It's like looking for Lombard ancestry not in Lombardia or the Veneto, but in Calabria.
Also, what about the chronology here? When did this supposed movement take place? How does that fit with the development of the language? How could the Anatolian languages, with no word for wheel, have entered Anatolia for the first time at such late dates?