[wqaatwt]

> there are basically no migration stories

Irish have migration myths.

So do Greeks (probably a bit more localized intra-Balkan movement, though).

To be fair IE migrations were very long ago. It’s not inconceivable that oral myths might have been preserved for several thousand years and yet we might know nothing about them.

> wouldn't have been particularly noticeable in any one life time

Probably not true. At least genetic evidence points otherwise. IIRC we’ve found individuals as far as Britain who were closely related (a couple of generations) with remains found in the steppes. At least some elite groups were very closely related paternally and moved very fast across Europe.