If you throw water in the middle of a crossroad soon its gonna cover all the streets meeting there, as each passing car picks up and moves some drops along its way. So I think its likely that it spread many times over and over, with each passing migration, not necessarily only in the Bronze Age. As for the initial expansion, I'm guessing one of the Central Europe/North Balkans cultures that were later at least partially indo-europeanized might have carried it. Which E-V13 subclades are you associating with those R ones you mentioned?