Burrard also did extensive testing on this using a large steel plate mounted on the side of a "Lorry". After reading through all his detailed descriptions consisting of numerous pages & illustrations the bottom line was basically a 40/40 situation.
The 40/40 term is mine not his but it boiled down to on a bird/taget moving at 90° to the shot line if it does not exceed 40 yds range & is flying no faster than 40 MPH just shoot, DON'T WORRY about the 3-dimensional Shot String. Under these conditions the elongation of the paterns were so slight as to be essentially meaningless. He of course only tested the 12 ga, might not hold true for a .410.
A target moving at any angle other than 90° to the shot line would of course have even less sideways movement across the shot line than the 90° one. For the most part for anyone other than extreme range pass shooters, speaking of shot strings mostly just clouds the issues & causes undue concern. As Nash Buckingham so elogantly put it the main thing is to "HIT" the bird.