Unfortunately, the only way to change your SWTOR e-mail address is by calling Customer Service. You can try calling at a different time; usually they don't have this long of a waiting time.
By the way, don't forget that your SWTOR account is connected with your EA account, so if you change the e-mail address on your EA account, it will also be changed on your SWTOR account. However, I believe it is just as difficult to change an e-mail address on an EA account so try SWTOR Customer Service first.
