Got it after 3 tries with the new (old) Chinese vid.
Here's the real trick. The motions are important, but so is the orientation of the shirt and which hands to use.
As a righty, I got it working by having the shirt's neck face to my right, waist facing left, shirt front facing up. Grab the middle point with the left hand, and the shoulder point with the right hand.
Having the shirt going from left to right (neck to waist) or using my right hand to grab the middle, and my left hand to grab the shoulder (as I was inclined) would leave me with a nicely folded shirt, but with either the back of it facing up, or the front facing up but the bottom folded over the top.