I am going to try to break down my original thought about Thracian E-V13 because my wording might have been too abstract.
If E-V13 is a Thracian, and thus Dacian, marker then its great presence in modern Greek demographics has to do with the fact that the former have had great success in expanding over peninsular Greece, Vlachs being named as Dacians explicitly in historical accords, and also providing a good explanation for the big chunk of what is referred as "Paleo-Balkanic" admixture.
Modern Greeks look to be as much Balkanic (Thracian or related), or at least in the ballpark, as the qpadm models suggested by poster idontknowhatiamdoing.
I think Slavs brought in Peloponnese and to a lesser extend Arvanites. I cannot rule some ancient assimilated Ancient Thracians.
Goths in Iberia showed high E-V13 (25% to 30%) that they picked in the Balkans. Maybe the same will turn true in Peloponnese.