Do you think that getting the mushroom in world 1-3 is faster with the RTA route or with the " get the mushroom faster" strategy? I am not very sure, but it looks like the RTA strats is faster because you get running speed while with the second strategy, you have to jump over the gap, which results only in walking speed. I would like to try it myself, but I am not using my computer at the moment.
RTA strats: you get the mushroom from the box, but you don't collect it. Then you run back a bit, wait fir the mushroom to drop down, and when it is about to fall, you start to run and you jump into the mushroom, collecting it with running speed in mid-air so that you land on the other side of the gap:
http://www.twitch.tv/i_o_l/v/116301412?sr=a&t=156 (2:30)
TAS strats:
https://youtu.be/EDjGk5q-55M (1:40)