Misinformed, I exited the wrong side of Shinjuko.
oops
Shinjuku Station is used by an average of 3.64 million people per day in 2007, making it the busiest train station in the world in terms of number of passengers. …
For about a half hour I was entertained by the manswarm. Eventually I decided to cross over to my intended destination.
After another 90min, I finally gave up and went home. There seemed to be no way to cross Shinjuku East to West. In fact, I needed to watch this instuctional first. There are three different ways to cross.
Click PLAY or watch it on Vimeo.
Rick McCharles 
You should try Mornington Crescent; hope you are OK though.
I spent a week a block from Shinjuku station while competing in Japan. First time through I was with the group. Then learned to navigate it on my own when I had lots of free time. Fun and busy.