The Iwama weapons system has 7 ken and 20 jo suburi. In the linked video, the ken suburi are demonstrated. The first ken suburi is a shomenuchi. Could you post a link to a video which demonstrates the "first suburi"/"shomenuchi suburi" as you believe it should be done?
BTW, the jo suburi include the uchikomi series which includes shomenuchi: http://www.youtube.com/watch?v=O9U04EU_Qp8&t=1m30s