You may want to check the Gettysburg National Military Park Museum. They have a Whitworth (minus the carriage) in their collection. They should have reference material and potentially provide you with much material on techical data that they may have. Remember it was manufactured in Great Britain so their version of the "National Archives" should have material in reference to contractors and the contractor should have contracts, techical specification, etc. I hope this will helps.
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment