Update:

Was able to get my own account through using the F5 refresh trick (when the server list finally displayed Zalera as a destination rather than just a limited world list).

Just to explain to those who don't understand the process, let me make it clear:

1) When you choose the optional services then click on "World Transfer Application" you will likely often get the message "There are no characters eligible for transfer" or something like this. I'm going to refer to this message going forward as "Error 1"
2) Select, from the list of destination servers (top drop down) first. If the destination server you want is unlisted, I'm going to refer to that as "Error 2"
3) Select, from the list of current servers the one that has the character(s) you want to transfer. If the server you want to transfer FROM isn't listed, I'm going to refer to that as "Error 3."
4) Finally, select the "Yes" radio button on your character that is transferring.

Any time you get Errors 1-3, you refresh THAT PAGE without clicking any other page requests (i.e. back, forward, clicking on the icon for mog station, logout, etc).

All 3 accounts I transferred this morning took under 5 minutes from the time the application was submitted until I got the confirmation e-mail back that it was completed.