"My hypothesis" was not however, that only "pure Germanics" came in, but Northern shifted people in Late Antiquity and afterwards. So this actually includes e.g. Frankish people of Gallo-Roman descent, Pannonians of Illyro-Celtic descent, Bavarians which became part Celtic-Slavic and so on. Like if a Frankish noble took servants and artisans, a whole entourage with him, that too, would have been, relative to the population of Imperial era Rome, "Northern shifted". Like Slavs from the Balkans too were not "pure Slavs" necessarily, but still a half Slav-Balkan Croat, to give a concrete example, would have been fairly Northern shifted relative to most of Italy at the time in question.
So basically its always what was present at time X in place Y vs. time Z in place Y. If they were newcomers to a region, let's say the region of Lombardy, I would count them, regardless of whether they are pure I1 Scandinavians and Viking like or not. What changed is the flow. In Imperial times it was mostly from the East Mediterranean and North African provinces, with further reach, from Late Antiquity on it was more transalpine, to put it that way. That shift was caused by Germanics, but it was not just "pure Germanics". Like you can see in Szolad and Collegno, there was some variation and mixture in them as well already, and that being said even without artisans and other specialised they might have called for from transalpine regions, which might have been even more mixed than they were. That's why you see more Celtic-like and Slavic-like admixture too.
I'm really curious as to what more complete early Medieval cemeteries in Italy and elsewhere might look like. I guess many, many samples will be like Szolad and Collegno, with recent mixtures where you can see someones great-grandmother was a Slav, or a grandfather a Lombard and so on. And this will be a widespread phenomenon. Actually more than the wild mixture of the outliers from the Imperial Roman sample, because they didn't make it en masse up to the Northern provinces, while this trend will make it down to Sicily.