Now for the E-V13. At that stage I think they belonged to a group from NW Ukraine/Moldova that lived between the steppes and the Northern Carpathians in the early Chalcolithic and early acquired and specialized in high-altitude cattle breeding, which was a special skill - perhaps through contacts with medium strict, perhaps for another reason, and they may have acquired some other specialized skill that helped them play a leading role in the Chalcolithic revolution in the northern Balkans; we will probably never see them in an urban environment or within their own remarkable material culture( Paleo: that means not in southern Balkan until IA), but they participated in the Chalcolithic revolution in the company of some essentially Mesolithic groups of European hunter-gatherers who stood at the forefront of the Chalcolithic societies of the Balkans and E-c13 are part of their company and have some early entry into the Balkans from the northeast during the Late Chalcolithic, preceding the Indo-European migration. It is possible that you are right and that their second entry into the Balkans was in an Indo-European context, in the Early Iron Age, again from the north, in the context of replacing Thracian elites with Dacian ones. Now, how they ended up in the N Carpathian/Ukrainian Steppe area, in the company of various Mesolithic European hunting tribes, since they are clearly Natufian descendants (?) is beyond me, but they have an old presence in the zep. Ukraine/Dniester/Carpathians and quite obviously, unlike Neolithic farmers, had no problem integrating into the emerging Indo-European communities.
This means the main expansion, the one which lasted, was with Channelled Ware in the EIA. But E-V13 appeared before, presumably with earliest GAC and Ustovo-Gorodsk/Cernavoda intrusions. This suggests, pretty strongly, they were centered in a subgroup of Tripolye-Cucuteni and marched with Northern intruders, like GAC and Western steppe warbands.
Associating them with either a subgroup of TCC, or a pastoralist people related to Bodrogkeresztur-Tiszapolgar, Petresti is the obvious solution to the problem. Just like GAC, they were already closer, in lifestyle and customs, to the PIE than the settled farmers of TCC and the other Copper Age populations. So they could weather that storm and made alliances with the newcomers.
This means we got splinters in the Balkans, but that was, like I always stressed, not the main and core population, but just splinters which bled into the Balkans, which moved South like transhumant Vlachs did, or with other companies. But if they would have stayed in company, what is the sole option in the South Eastern Balkans to have survived, then E-V13 would have been demographically much smaller, weaker and correlate with other haplogroups. Both is not the case, which means the Carpathian homeland is the right one, as this commenter from Bulgaria already claims himself.
The big replacement in the Balkans came in the EIA, which means 100 % its Gáva-related Channelled Ware. And that's clear if looking at the background of the South Thracian samples: They are from the post-Psenichevo context for god's sake! That's in many respects a carbon copy of earlier Channelled Ware groups from the Lower Danube, like Babadag I, similar to Lapus, Belegis II-Gáva and Vartop too. That's their affiliation, not with the older local elements in the region.