I think I can be wildly relevant. I work directly where you are talking about, and commute by car from Petworth. I often drive my wife to work, and go from there though (Van Ness)
Your best bet is north on Connecticut. It is a piece of cake, and will move quickly the whole way. Get on 495 North, and take the 270 spur exit. 495 will move well, you will go somewhere between 20 MPH and 50 MPH, depending on traffic, but it WILL move. Presumably you are in one of the big office buildings inside the triangle, so take either Old Georgetown (first exit off of 270) or Rockledge Dr (2nd exit) and that puts you there. Should be about 30 minutes, maybe 35.