Since you can't log into your account, and it looks like you are trying to avoid using a "government issued ID", I'd recommend giving them a call. I've had both good and bad experiences while calling Battle.net/Blizzard.
North America
Hours: 10 am - 6 pm Pacific Time, 7 days a week
1-800-592-5499
Here is the full list of contact information
This was taken from my answer in another post on arqade.
Do note that sometimes they may ask for some personal information.
