I do not think this "current wold is full try again " nonsense has anything to do with the actual amount of people on a world. I've gotten the message several times right after I hit the start button and before any of the world information populates. How can it register my information before I have picked a world to load a character from?
FFXIV probably connects you to the lobby server after you select 'start'. You enter the lobby and select your world server from there.