Yeah, you're right. I don't think you can change the character which was designated during the application process.
And the Application page does confirm this from the looks of it:
  • Only the data of the character selected during the application process can be copied.
  • You cannot change the character you selected in your application.
I do wonder why it is a no-no...
Shouldn't be too difficult, I imagine?

All we can do, is delete the character and create a new one, or re-copy the data, but as far as I know, there is indeed no way of changing the designated character, for the time being any ways.