Wow, this is a bit weird of a thing to say, but verisimilitude is actually such a useful word to know, glad I know it now lol
I don't think they were mostly Anatolian Chalcolithic, I think they would have been a hybrid of something Iron Gates-like and something Anatolian Chalcolithic-like, before further blending with the EEFs they would have come across further West across the Mediterranean (none of these blends are necessarily 50/50 by the way). If I'm not mistaken, the right proportions of that blend would produce something Beaker-like - but the thing I don't like about autosomal genetics being so over-utilised is that so many blends can create the same rough thing, because after the migrations of people intensified from the Late Neolithic onwards everyone became so mixed up (at least relative to these "purer" populations like WHG etc.) - as one example, it seems like most in academia see Corded Ware as descended from Yamnaya, but there's so many lines of evidence to show that that isn't the case. Just because they are both approximately EHG-CHG hybrids, doesn't necessarily mean one is an extension of the other, as these ancestral profiles could have been (and I think definitely were) achieved in parallel. That's the main reason I really like looking at Y DNA for tracing male-dominant migrations, because the precision leaves no room for ambiguity, but anyway.
And I don't see early Vinca as too late: it's from the 6th millennium BC and has the earliest known example of copper smelting. With a migration of some of these metallurgical folk from early/middle Vinca to West Asia (perhaps in the search for new finds of metal like has been speculated with the metallurgical Beaker folk, who knows - this also works with the idea that they would be nomadic pastoralists, whose presence was known at least from Ubaid), Vinca wouldn't just collapse or become significantly less advanced or anything like that - you wouldn't expect to see much of a change at all, as the Vinca people proper (the mainly EEF farmer population) were advanced in their own right (as I said, I think the proto-writing, despite swastikas in the Danube script, surely has to be attributed to them, as to put it bluntly R1b-M269+ folk and literacy didn't get on very well until even well after the Iron Age in some cases).
This puts a migration out of the Balkans to West Asia of these metallurgical folk somewhere around perhaps the year 5,000 BC if I had to guess, which leaves 1,000 years until the L23 mutation comes along.