the shift you see on that pca couldn't also just be because of inceased iranian farmer/CHG or steppe related ancestry? the filled green triangles on the upper right corner are if i remember correctly iranian farmers or CHG. they and the steppe were not that high in east eurasian ancestry.
the old study you quoted also found that "By that method, for Y-DNA, Alu, mtDNA except Iraq (13%) and Armenia (6%) for females, the Central Asian contribution to the hybrids (Armenia, Georgia, Northern Caucasus, Syria, Iran, Iraq, Lebanon) were similar or even higher than to those of Turkey and Azerbaijan."
the "central asian" detected here might not all be real central asian turkic ancestry.