Brief update on Veteran's Affairs and my GI Bill application:
I did contact my congressmen and women (like my friend Russ suggested) and two went to bat for me. Representative Lloyd Doggett and Senator John Cornyn did in a matter of weeks what I was unable to in nearly six months. Namely, reach anyone at the VA. After my congressmen got my claim approved, payments activated and all my back pay, Angela at Rep. Doggett's office even managed to produce a letter from the VA acknowledging their mistake and ultimately put an end to their cancellation + overpayment letters.
Thank you congressmen and thank you even more congressional staffers.