This is an interesting problem.
Since your requirement is just for the printout to be that way, I would be inclined to use a macro to print the document. The macro would basically specify the print order (eg print pages first page, last page, the rest of the pages).
Another alternative is to simply bring the sign in page to the front of the document and after printing the document double-sided, turn over the top page of the print out.

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Andrew Lockton
Chrysalis Design, Melbourne Australia