I'm not sure what you are trying to do. The two videos you posted are for turning a flat (2D) photo into a stereoscopic image. AKA, stereo conversion. What I think you want to do is add 3D text to a stereo image or video.
There are many ways to add stereo text to a stereo image. Any 3D graphics program, such as Blender, can generate 3D text (usually a 2D font extruded into the 3rd dimension) which can be easily layered over either a 2D image, or placed into a 3D scene.
"More specific is there a way to create the illusion of depth with say white text on a black background?"
If you just want 2D text to appear at a given depth in a stereo image, then all you need to do is offset the text slightly in the left or right image. You could just experiment with the amount to offset the left/right, or calculate the geometry of your video scene and position the text at a specific depth. It would be then layered over the video in the final render by your video editing software.
If you want to create text as 3D objects with depth, Blender could do that easily.
You can also precisely position the text in a 3D space with Blender's add-in stereoscopic camera.
Tutorial for making 3D text in Blender:
https://www.youtube.com/watch?v=gYXSo2xDUPEThe Blender stereoscopic camera setup:
http://www.noeol.de/s3d/"The idea is to create an information screen or menu for a 180 degree 3D video"
A menu like that would essentially be a 2D object (flat plane) in the 3D space. The text wouldn't need to be 3D, just 2D on a plane in the 3D space. Again, you could use a variety of software to produce the menu as an image, offset in the left/right stereo view to a desired depth, then layer that over your video in the final render.
If you intend the menu to be interactive, then it will depend on your application for viewing the video, which should have an API that describes how to make an object interactive. If not interactive, just information, then again it is a matter of layering the object (whether 2D or 3D) into both the left and right video, offset slightly to the left or right in the left/right videos, to position it in the 3D space.