I had been dealing with the busy line for about 4 hours. I finally found EA's customer support number and was able to get right through. 2 menu options later and I had a rep on the line within 2 minutes. Just make sure to choose SWToR from the first menu option and it will forward you to swtor support. I only was on hold for about a minute.
EA's support number is 1-650-628-1001
Try the above