In page 124 of Jon Speed's "Original Oberndorf Sporting Rifles" there is a factory drawing of the Type E (English) barrel profile used on rifles made up in calibers from .250" to .350". It's pretty dim and I'm not sure it would scan legibly, but I am willing to give it a try if you will let me have your email address.

Jon Speed says 6.5" to .404" in the text, but the label on the drawing clearly says ".250-.350 u. 6.5-9" The barrel length is given as 600 mm (23.6").