Meh. Friday after Thanksgiving. Nobody is going to be working Downtown. Provided its a domestic flight where you don't have the hassle of passport control at the checkin counter, I'd not feel uncomfortable with getting out of the "Phone Booth" at 8:00 pm for a 10:20 pm flight.

I'd definitely Uber or Lyft it. Be advised that there may be pretty high demand for Uber or Lyft that time of day and quite the surcharge may be in place.

You could just try for a regular DC cab...