It's not like they need to make 12,000 people younger all at once, I don't see how the 6-people-at-a-time limit applies here. You could make an appointment, get young-ified, instant results!
I do find it amusing that you're defending Star Trek writer's lack of imagination by citing their own meaningless techno-babble. "The solutions where they use the transporter buffer explicitly only work because no one else has used that particular transmission system between the problem and the solution." What in holy heck does that mean? Better reverse the polarity of that sentence!