I think the lesson here is that it depends on your trajectory - there's no one good way - and the bottom line is in a panic situation we will do what muscle memory tells us, so unless we go to stunt school (like that guy in that NYC bike lane video) it's sort of a useless discussion.

I should've let go of my bike - if I had, I wouldn't have had such bad sprains. (I thought it was 100% by now until I tilled up my garden last month ...) Falling to the side, probably it is best to keep holding on (and keep braking).