Well I think the L51 mutation was originally West European but I get your point, I do think it ultimately came from West Asia. In this theory, what would become L51 would split off around the modern-day Turkey-Syria region, then following the path of the previous Megalithic people across the Mediterranean, and introducing copper smelting technology and hierarchical systems (epitomised by Los Millares). So, the Asian ancestry you would expect to see among early carriers of L51 would be more Anatolian Chalcolithic (Cypriot-like if I'm not mistaken) than anything else - you wouldn't expect especially large amounts of Iranian or Levantine ancestry. Probably not by coincidence, the Beaker folk were Dinaric, which is a very modern phenotype that traces its origin likely back to the same Syro-Anatolian region.
As for the Steppe genetic signature being different to the Vinca one - if I'm honest, I have no idea about this, as I just take Steppe to mean Steppe, though I understand it is a hybrid population reference and not "pure". All I know is, the Balkans had a very large presence of R1b just before the Neolithic incursions of farmers from Anatolia (so far though, only the presence of V88 has been shown, but the rest can be inferred), the Vinca culture had the swastika and copper smelting technology (both of which it later spread to West Asia, amongst other things like unmistakably distinctive figurines and perhaps proto-writing (although I doubt proto-writing and the figurines have anything to do with these R1b guys, but rather the farmer population that made up the bulk of this theoretical population migration)), the more "archaic" branches of R1b-M269 are Balkan, the Areni-1 Armenian Chalcolithic samples (with red hair, blue eyes and pale skin - surely a sign of links with R1b folk despite being of typical Caucaso-Zagrosian Y DNA) showed unmistakeable European Hunter-Gatherer ancestry etc. - I've said it more to you than any other person so you get the idea of why I believe in a Late Neolithic-Early Chalcolithic migration from the Balkans to West Asia.
If Iron Gates is used as a proxy for what these original Balkan M269 folk would have been like, then there would be a relatively high WHG:EHG ratio amongst the obviously much later Beaker folk - higher than can be explained easily by a simple mixing of Bronze Age Steppe with European Neolithic types. I think this is the case, which is nice, but don't quote me on that.