The Hornady seater die arrived today, so I loaded a 2nd batch with the 71gr Berrys. These all seated perfectly straight! Couldn't be happier with the results. I don't have a concentricity gauge but they all look perfectly concentric to my eye which is all I could ask for.Are you getting the bullet's to sit up straight in the expanded case mouth? Or are they lolling off to one side? If they are sitting straight up but seating crooked, the die is tilting them somehow, and it should be possible to figure that out and correct it. But if your bullets are not straight up and down as in the right side illustration below, then something is amiss in the flaring stage, such as not getting the M-die expander deeply enough into the case neck or else the step not being wide enough for the Berry's bullet, or simply not setting the bullet into the open mouth firmly enough.
I think you make a good point about not going deep enough with the Lyman M die. I went a little deeper with this 2nd batch which seemed to make it easier to align the bullet straight on top of the case prior to seating.
Thanks again everyone! And +1 on the tarp!!