We have to admit, the plan to build an expensive, mock Enterprise interior on the ground and lure Kirk there because he once had meningitis is bat-ass crazy for three reasons:
• If you can get Kirk down for an official visit, you can "incidentally" talk him into a blood draw with some story about medical research. Say you're looking for the perfect antigens to cure a dread disease, and they aren't found in Gideonite blood. Bam, he's rolling up his sleeve for you.
• You don't even need Kirk. Just message the Federation that you are conducting medical research and would like a live sample of that virulent meningitis pathogen.
• And the whole plan is crazy, because a pandemic that kills so many people in a short time would devastate the economy.
You forgot reason #4: On a planet where overpopulation is so rampant that people can barely move, building a 1:1 scale Constitution class starship on the ground, and have it completely empty, would have caused the masses to try to break into it simply to have breathing room.