More than shutting down servers for travel, SE needs to do what they did with adventurer in need but for DCs.

Set up a system where the DC with the lowest population at any given time has a boost to gil and xp for all content you do through the Duty Finder while not in a premade group. Encourage people to travel to dynamis to fill out their queues for better rewards.
Time and time again it's been shown that punishing unwanted behavior in players doesn't work, the only thing that does work is rewarding the behavior you do want, which is evening out the DCs populations on any given day so they stop crowding a single DC.