Basically, I am making a beta design for a security mechanism which I will use in a survival server. I want to make it so that when the puzzle is completed, it will turn OFF rather than ON. Therefore, the doors will open rather than close. This is the video which I use as a guide, and this is a copy of the map I use.
All you have to do is remove the signal inverter that uses a redstone torch. Here it is in the video tutorial (at 5:30):
All you have to do is replace the torch with redstone, like this:
As you can see, the doors are now open, even though the visible redstone is powered off. You can do everything else as it is in the video.