I believe you have to argue:
a) You were incorrectly characterised as a no-show on your originally booked ORD-PHX flight - you should be characterised as a misconnect because AA literally detained you on their GRB-ORD flight
b) You are due a refund on the ORD-PHX segment because AA failed to book you into next ORD-PHX flight, if what donotblink said is correct.

I don't think you can get ORC after (b) happens
Nor full indemnification for your UA airfare
(unless as a goodwill gesture)