Based on last year's calendar and the last seating time for Carthay, I think an 8:00 pm closure is likely for both DCA and DL.
Whether it would be a waste or not is harder to say. I don't think there is anything wrong with spending the last hour at a meal, especially if it's something you want to do. I haven't eaten at Napa Rose or Steakhouse 55, so I can't say if one is markedly better than Carthay Circle. I do like Carthay Circle and I think it would a wonderful place to have an Anniversary dinner.