Guide (Warning: Long read, strat is expert difficulty):

So just to preface, for clarity's sake, the setup for this strat starts after you've done the first step in completing the puzzle in this room, by getting a box up to the mid level and in position to be grabbed on the top level during the next reverse gravity cycle.

Step 1.

So this strat is a case of losing time to save a lot more in the end. In order to have time to perform the catapult strat with the upper box and make it through the big door before it closes, you have to push the lower box ALMOST all the way up the big slope. I say "almost", because you do not want the box to bounce off that right wall at the top of the slope at all, since doing so will send the box quicker back to the left, which will, by extension, cause it to build momentum much faster down the slope. Instead, you want it to be carrying momentum UP the slope as you jump away from it, so that it starts sliding back left as late as possible with as little momentum as possible, giving you that aforementioned maximum time to manipulate the other box. This might all be obvious to most people, but it is crucial, so I felt it was necessary to explain just in case.

Step 2.

Next, you want to use just basic optimal movement to get up the ladder to the top level. Once up top, you then have room to do four full jumps to the left towards the other box. You want to grab the box as soon as possible and begin pulling it right. This is where things get tricky. There are three key components of achieving a successful catapult:

A. Timing the Box Climb

You need essentially perfect box rotation over the corner of the overhang to set up your best chance at achieving the next step, which of course can only be done by climbing the box at the right time. I achieve this using a visual cue. You will notice some sort of bolt sticking out of the wall, just above the overhang. I draw an imaginary line straight down from the rightmost edge of the bolt, and once the rightmost edge of the box touches that line, you want to let go of the right input to stop pulling the box, and immediately press and hold the jump button until just before the boy begins to stand up on the box to ensure the quickest climb, after which you want to begin walking left across the box as soon as possible, causing the boy to automatically grab the wall, which leads straight into the next key component.

B. The RMJ

Once you've walked about 2/3 of the way across the top of the box, you want to simply perform an RMJ and hold the jump button until it's time to fly. Unfortunately, this is the part that makes this strat so inconsistent. You never really know what you're going to get. The box might rotate too fast, too slow, not at all, and sometimes the box will just straight up eat your jump, which I haven't been able to understand just yet, if it's even possible to. It can be frustrating, but like I implied before, perfect box climb timing does increase the success rate. Anyway, you're looking for the RMJ to cause the specific box rotation speed shown in the video, so that the boy grabs the first corner of the box available to him after turning around, tries to climb it, causing the box to rotate a bit faster, in turn causing the boy to let go before finishing his climb, and then finally just barely grabs onto one final corner of the box, pulling it down and causing enough box rotation speed to propel him across the gap and under the door as it's falling. There's a catch though, which is the final component.

C. Letting Go

That's right, as I alluded to before when I said you have to RMJ and hold jump until it's time to fly, the launch from the box doesn't happen automatically, you must manually time your dismount, which might seem pretty hard, and it is at first, but it definitely becomes one of the easier parts with practice. As you can see in the video, the boy grazes his head on the ceiling and still makes it, so there is a moderately generous window you have to work within, but my advice is to let go a little earlier than you think you have to, as I've noticed there seems to be a bit of lag between releasing the input and the boy actually letting go for some reason.

And that's pretty much it. Feel free to message me with any questions or comments, including any ways that I can improve this guide. Thanks for watching and reading!