I either copied it wrong or entered the wrong number. The best things is that the blizzard account help 800 # is jammed with RMAH complaints. So now I'm locked out of my account... Any suggestions?

You should be able to go through a process that is similar to "I lost my authenticator". I can't remember where it is but I think it is in the FAQ.

In order to sign up for the SMS stuff to back up the authenticator I would have to log in. Which...

Are you using an Authenticator-App? If so, have you tried to resynchronise your Authenticator? I once thought I added it wrong, but all I needed to do was to synchronise it again.

It says sync successful, but it still does the revolving serial numbers. It doesn't show my number.

What do you mean revolving serial numbers? If you mean a number that changes every ~30 seconds that is 8-digits that is your code. The serial has 14 characters with 3 hyphens. (Or at least mine does. Seems to start with 2 letters for region. i.e. US-XXXX-XXXX-XXXX)

In the 'Help' of the mobile authenticator.

'Locked yourself out of your Battle.net Account?'

'1. If you have the restore code and serial number from the last installation, you can perform a restoration of that installation.'

'2. If you do not have the restore code and serial number from your previous installation, you will need to contact customer support.'

So i have the Restore code, but I haven't figured out how to use it on battle.net. Every time I do some recovery link, it just asks my to reset my password. There is no link for authenticator help.

Plus they want me to send a government issue id...

Yep, hope you didn't use a fake name for your Battle.net account.

it won't give you authenticator keys unless it synced with your account properly the first time will it? Are you sure you're using it right? no offense, it just seems like a super foolproof thing to setup.