AP would rather work around a complete gen case (that includes the caseback), meaning they might even provide the missing calibre if your case serial actually corresponds to the reference you’re looking to build. That part however looks unlikely, unless you got very very lucky. So even if you get a gen movement, AP
are not simply going to service the lot and issue you papers. Hence, you’re better off buying a second hand gen if you were after the papers, or simply enjoy the building process if you’re into this hobby for the right reasons. Many longstanding members and newbies alike can afford the actual gen watches, they simply prefer the collection/building process to visiting an AD.
legend is probably an exception here, as he likes to build watches for other members but prefers the cleanliness and pedigree of the AP factory.
QueTip is in his own exclusive league as he probably part owns AP.
So in all truth, for most this game is really about creative motives and hand-on approach preferences, and not papers and gen-like pass-ability. Which kind of a hobbyist you want to be is up to you. But be careful to not build something that you will then go on and sale online as gen as you will be spotted and reported on the day by half the community here