We didn't finish that chapter yet, there is a possibility E-V13 to have been a lineage of highlander population of Haemus-Rhodope which swept during LBA adopting Urnfield way and had the upper hand. Equal possibility as the Carpathian Basin. No one knows who was the actual winner culture. There is glimpses, but the actual influence is unknown so far. Sorin the Romanian archaeologist considers Stamped-Ware to be a different phenomena than Channeled-Ware. I don't think he has an agenda in that. So, we should keep the books open. This part here gets very confusing and i believe only aDNA can solve it. Archaeology has given enough but it has its own limitations.
Also, all i am remarking is, i think you are biased on your judgement, even if an E-V13 gets found in Iron Age Polynesia/Australia (figure of speech) you will jump in to say either a Dacian or a Slav from North Carpathians.
Its all about the phylogeny of E-V13, both your first and your second paragraph. If there would be an E-S2979 in Polynesia, surely he must have come from North Thracians. That's the point, they have such close TMRCA's, there is no other option. In all those cases you can just try to search for how they get to a place, not where they were coming from. That's fixed by now.
Concerning the old E-V13 origins, the same applies here insofar, as we know that the E-V13 population was huge for its time. It did compete with I-M253 in size, was larger than J-L283, and second only to the big Indoeuropean branches of R-L51, R-Z282 etc. in its time in continental Europe.
Now if you consider this, you need a natural habitat and demographic base which could carry such a male population! It can't be a small group which got pushed around and conquered multiple times, in an area which had an actual hiatus in the archaeological record and settlement history, at a time when E-V13 reached almost the level of R-L2!
Obviously I can't completely rule it out, but the Tisza zone is just the most likely source region because they moved to all those places where we find Channelled Ware, Daco-Thracians and E-V13 later.
The main question for me is not whether the Transtisza zone was dominated by E-V13, but only when other regions got their share from it. Because its not just Gáva, Gáva was the peak and its apparently also the time when the E-V13 growth peaked. At that time, the local groups in Bulgaria were either shrinking, overrun or not growing at all.
However, we had not just one incursion from the Tisza-Danube zone, the Eastern Carpathian basin, but multiple ones. Therefore Gáva kind of pushed relatives forward, which in turn pushed other groups with which they overlapped. The basic groups were Verbicoara (cremating group, related), Tei (unsure), Coslogeni (Sabatinovka with Monteoru and possible Wietenberg influences), Encrusted Pottery groups and Brnjica.
Therefore the real issue is not whether Gáva-Holigrady and Belegis II-Gáva were involved, because I have little doubts about that, but whether other related groups, which split off earlier, and moved into Bulgaria earlier as cremating tribes from the Carpatho-Balkan block, were as influential or at least in the South even more influential. That's the real question.
An isolated group in South Western Bulgaria is a much worse candidate, by comparison.
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