I agree about the sleeves, but I get much better results if I grab it at the bottom to shake it out. Ideally, there are seams coming straight down the sides from the armpits; I hold it where they meet the bottom hem. Note that whether you shake from the shoulder seams or from the bottom, one hand will already be in the proper position from turning the sleeves inside it; it's just a question of which one.

I also fold the shirt while standing, so I never actually need to lay it flat. There is a standing-only variation of the method that you cited, although I actually use a different method that begins from precisely the position that I'm in when I leave off the shaking.

In fact, the idea of actually laying something flat before folding strikes me as a greater source of inefficiency than anything else being discussed here. With practice, you can even fold bedsheets in the air.