in the 2nd video, what rpm were you where the sputtering is VERY pronounced ? RPM where the sputter was slightly pronounced ?
Need more info about this fuel shutoff issue. When the modis is hooked up you can read what the fuel shutoff is doing in real time right ? When you see the fuel shutoff coming on (fuel shutting off) you'll hear a sputter, check to see if both the sputter and the command for fuel shutoff are in sync with each other. If they are, you have found your problem. You can also take a screen shot with the modis while you're driving, that will also help with diagnosis of this problem.
It doesn't sound like a timing issue to me, sounds more like fuel related, as it is very consistent when sputtering.