Now that we have the lovely ability to delete our own dead alts, I decided to give it a try today and after quite a bit of hunting and searching I finally found the steps to do it. Once you find it, the process is really simple. So to save others some digging, I thought it might be useful to just post the steps in the process.
First switch to the character you want to delete.
Next go to the very top of the page and click on Settings:

Then click on Delete Account. It will only delete for the character you are currently logged in to:

Finally you get the confirmation page. Be sure you want EVERYTHING from this character gone because it deletes it all. If there is writing or art posted by that character that you want saved, be sure you already have a back up. There is no turning back after you confirm!!:

Tadaa!! Three easy steps and the character is gone. You will have to log back in to your main account after this process.