Balmung is the most populated server and because it is so overpopulated, as you've seen it's pretty difficult to get onto. Other servers you can try early hours of the morning, but I don't believe that trick works with Balmung because of just how overpopulated it is.

The only ways to get on it are either straight away after a maintenance before too many people login, or to simply create your character on any other world, wait 3 days (it's a transfer rule) and then just pay the world transfer fee to transfer across. When you do a world transfer you can select any server, even the locked ones and since there's no planned scheduled maintenance any time soon, this is really your only option to get on that server.