you have to switch between the first screen of char creation (race, gender, clothing, name) and the second screen (appearance of your toon). If you click "next" on first screen, the SWG client checks if your choosen name is available on the server. So you keep the connection alive. Just don't finish the creation of your new character and switch back to the first screen.
Do this name check procedure approximately every 10 minutes. I did it every 5 minutes - just to be sure
You have to do this until the GM have responded to your ticket and restored your deleted toon. I had to wait 3,5 hours or so until they finally restored the toon and i was able to complete character creation of the third one.
Of course you should not do this if there's a server down. I believe character creation would not work if the server is offline.
Yeah - it's boring to klick every 5 or 10 minutes for a few hours (maybe not if you write an Auto-It Script

). But hey - you get a third character slot!