I noticed the description/hint for the puzzle "Now you see it" in the 1st post is a little off.
Here is how it works:
There is a way you can use the single cube in the alcove around the corner to solve this puzzle. You don't need to bring one with you.
When you first enter the puzzle's area keep you eye on the shut door you need to open and NEVER take your eye off of it. The moment you turn away, the door will change to a location that warps you back to the "Don't Look Down" room. As long as you keep the door in view you can walk around the corner into the alcove and grab that cube and use it to open the door. Just never turn away from the door and it is a piece of cake. It took me a while to figure this out.
I am still amazed that I managed to get through the whole game without looking at a FAQ/walkthrough