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][1]

This was taken from [my answer in another post on arqade][2].

Do note that sometimes they may ask for some personal information.

  [1]: https://us.battle.net/support/en/article/contact
  [2]: http://gaming.stackexchange.com/questions/85240/how-can-i-contact-blizzard-support-without-login-to-my-account