You don't say were in New Jersey you are leaving from, but if you do leave at 2 am, you can take I-95 all the way south to I-10 and avoid DC traffic. We travel from GA to NJ and back multiple times a year. As long as we leave by 3:30 am at the latest, we easily make it to Fredericksburg, VA by 7 am (averaging 74 mph) and avoid all the traffic of Northern VA and DC. The rest of the drive is smooth sailing. We leave from South Jersey (30 minutes from Delaware Memorial Bridge) and usually leave at 3 am. Same thing for the drive north lave GA at 3 am and get to NJ by 3 pm. That's making only 1 stop for gas, food and potty.
-Michael