Have you consdered putting a real email address in rather than one which gets converted to text messages in 140 character segments? It seems to me that would be a simple solution, especially since you have an iPhone and an iPad which can both handle email...
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iMessages are resolved by an appleID, an iCloud account or a Carrier phone number.
If you have an AT&T call number that is active on the network, then obviously you want to use that to receive iMessages on your phone. Then you will want to set up the iPad to receive iMessages via your appleID which requires email verification from your iCloud email address. You can resolve this by verifying your apple ID with your iCloud email account on the