I'm locked out of my iPad

We have a 3rd Generation iPad that we bought for our kids back when they first came out. about a year ago, I created a new apple ID and password for them so that I could text them from work. Since you cannot create an account for a minor, I faked the birthday to make the account appear as if for an adult. I never wrote it down. big mistake. I forgot the password so when I attempted to change it, I was given 2 options - have an email sent (which I am locked out of without the password) or go through the security questions (which start with the birthday). So I have neither the password or phony birth date. As a last resort, I tried restoring the iPad but apple account is still linked even after a restore. Now I am totally locked out. Called apple support but they will not help without paying for it. There must be something I can do to get on this thing. Any suggestions would be much appreciated.