I found a list from the Horimachi Watch Club that extends some of the info for the original Captain Cooks reference numbers to at least some of the later movements:
<Captain Cook Ref.number>
770 Captain Cook
727 Captain Cook Ladies
11683 Old Captain Cook (AKA Mk I)
11773 Captain Cook ((AS1789 ( 1700/01 ))
11773/1 Captain Cook (AS1700 series 30 jewels?)
11773/2 Captain Cook (AS1902 25 jewels)
11868 Captain Cook Day Date