If union rules prevent crew from flying a charter (there are plenty that operate out f O'Hare BTW and cost around $2000/hour for a good one) then put crew on the airliner and give the charter option to the bumped pax. Would still have saved money/reputation.
Just like to add for NoFly; I take it you believe that the interview with Oscar Munoz is fake news? Seems pretty clear to me that he agrees with the majority here that this should not have happened. He sums it up when he says that his staff have a lot of common sense but were prevented from using it.