To me, the easiest way to save face is for Rock to acknowledge the elephant in the room.
Come out and cut a promo essentially running down all the reasons you want/need to fight Roman. That you wanted to do it at Mania but didn't realize how much people wanted to see Cody get his moment, you see it now, and that it's Cody's time and Rock can still deal with Roman and have his match later. Cody gets the match, and Rock then runs down all the screwy finishes Roman has gotten away with and to make sure the match is fair this time, Rock announces himself the special referee.
Cody gets the match, WWE still gets the Rock promoted as part of the Main Event, and you can still do Rock vs. Roman down the line.
That's assuming they want Rock vs. Roman as a singles match. It's still somewhat possible (Though I don't think this was planned in advance) that they want a Triple Threat so that Cody and Roman can cover for Rock's conditioning.