HOLD THE PHONE!  I just found the solution for doing that same edge connection cut with and automatic quad production!  I was not using the Subdivide tool in Blender correctly!

The key to making the same edge connections in Blender as you see being done at this point in the tutorial video by Luxxeon here:

http://youtu.be/ErtmvdOLFZg?t=5m4s

The way to do it is to select all the same edges, then use Subdivide to make the edge connection.  However, you must remember to enable the Quad/Tri Mode ticker box in the subdivide option menu in order to get the same results! You could change the type of quad it produces too.  If you want one much like the video, you should use Inner Vert option as the Quad Corner Type!

If you don't use the Quad/Tri ticker, then the cut isn't the same, and you need to use the knife tool to finish it off.

Blender is amazing!  Thanks again for the tutorial.