Use the retrieve account name function on the main site to check that the registered emails are correct: http://www.worldofwarcraft.com/login...ount-name.html
That'll automatically send an email, assuming the email you enter is registered to at least one of the accounts.
If you don't get that, you have a problem with the email. If it gives no error on the page, then something's probably filtering it (happens a lot with comcast and yahoo for some reason). If it gives an error, you're checking the wrong email.
If the email needs to be changed, you'll have to call billing. Account admin will only send you a message that they won't talk to an unregistered email if the email you sent from isn't the registered one (the message received thing is automatic and doesn't mean that you sent from the right email).

On your gf's account... well you might not have played it, but by transferring to it you were claiming that it was yours and subject to a ban if it was not. Last name is simply all the computer checks - the rule is only transfers between your own accounts (ie Bob Smith registers one as Bob and one as Bobby and the computer doesn't care, and it's within the rules.... Bob & Sue Smith transfer and the computer doesn't notice, but if anyone looks, the rules are against it and both may be banned - in theory). However... it again doesn't really fit what the GM said. Is there any software that might be installed on her computer as well? Any game optimizers or such (many of those have functions that can be used as speed hacks and WILL trigger Warden)?

However, they usually go about problems with the registered names in a slightly different way. It doesn't honestly sound like this is the problem (though it may prevent you from retrieving the misnamed accounts even if they do unban them and it IS a bannable offense waiting to be caught). Unfortunately if the G15 or autohotkey ever did cross the line, even temporarily or by mistake - it might have been only for a day and took them a while to process it all - they aren't going to tell you which. It would simply say 3rd party software/ automation ban.