This is a little different than your situation, but we were running late on the day of check out and knew we wouldn't make our 12:00 ADR at Trex, so I went to the concierge at the resort and they said no problem, noted it on our reservation, and indicated we would not be charged as long as we showed up. We were seated almost immediately once we arrived even though we were 30 min late.
Obviously Trex is not Chef Mickeys, but maybe if you're running late or know you're delayed and call the dining # to let them know, they will be willing to work with you? Or maybe not charge you if you couldn't make it because of matters outside of your control and it wasn't just a straight no show?