Hi David,
Once you have figured out how to get the square (or generally the polygon) defined by the tape, you could apply
ExtractPolygonalPrismData class, which "uses a set of point indices that represent a planar model, and together with a given height, generates a 3D polygonal prism". Can't say you how fast this operation is, but from my experience it works "just fast enough".
As for extracting the polygon... this sounds more like a task for OpenCV. Once you have applied their algorithms and got 2D polygon, it is easy to determine its 3D coordinates.
Regards,
Sergey