How can I fully complete Antichamber demo?

I have played the May 2010 demo of a game called Antichamber, formerly known as Hazard: The Journey of Life. Walkthroughs are available on Youtube, see for instance this one if you are not afraid of spoilers and want to get a glimpse at the game. Yet these are a kind of speedrun, and I would be interested in a complete playthrough of the demo.

Here is the map of the chambers at the end of my playthrough:

Here are the achievements I got at the end of my playthrough:

I have put red dots at the locations of missing chambers. I am not sure these are available in the demo, since:

1. Some of them are listed, at the very end of the demo, under a caption "Look at all of these unsolved puzzles." and a remark about the upcoming full game.
2. At the end of the demo, there is a no-return point when we get a binary gun (addition/subtraction), which would prove helpful in my opinion in some puzzles.

So, has anyone played this game already? And have you solved additional puzzles?