It was super easy.
I kinda wandered around til I found the incinerator, and then it all made sense. I used a trick where I put the pieces on the incinerator itself, portaled to the button, and watched as it started to slide, then fell in as the incinerator opened. Saved so much time.
I had trouble finding the final piece, because I didn't realize it was suspended, and then when I did my momentum jump to knock it down, I kept looking for it in the air to grab, then noticed it on the ground...