Regarding Hungary, my understanding is that post-Roman Pannonia (and Eastern Hungary) had a very high diversity of groups present (Langobards, Ostrogoths, Slavic groups, Avars, and many more) even by the standards of the Migration Era, and that's probably a good set of conditions for the language of whoever the earliest Hungarian speakers were (probably a long standing group from the rough zone of the Volga River) to take a place of prominence as a lingua franca and become common that way (they'll seek to recruit others who have no tongue in common and that way the language will be more likely to spread across barriers).
So you may be more interested in trying to replicate that kind of scenario than having simply one homogenous (but small and from far away) group spread their language to a single much larger population, where the most likely scenario is probably linguistic assimilation by the incoming folk.