I have not had a problem with powder migration when using AA style wads in straight wall hulls. Most of my loading is with flake powders and I haven't had any problems, even with some reloads I still have which date back to the late 1970s. These are 3" 20 gay Federal hulls, WAA20 wads, and Blue Dot powder. If one "candles" them, a particle or two may be seen on the wrong side of the over powder section but one would not know if it occurred when loaded or at some later point.
I have some other loads that utilize some clear Fiocchi or Cheddite hulls, WAA12114 wads, and Win 571/ Hodgdon HS-7 powder. Most of these have been bouncing around vehicles and pockets since the mid-1990s and they are much the same.
There are some who speak of very different experiences but I haven't had any myself. Nor have any of those I regularly shoot with that reload. For over a decade I was loading over 15,000 rounds a year of just 12 ga and a fair percentage of that used WAA wads and straight walled cases. If I would have had issues I would not have continued on that track.
