If you leave that museum at 5 or 6, it could easily take you well over 2 hours to make it to Quantico. SERIOUSLY. This is part of my daily commute.
28 from Dulles through Chantilly all the way into Manassas is bumper-to-bumper. If it is raining-it will be worse.
I urge you to be on the road by 4 at the latest. Also, when you go down 28 and approach route I-66, get off there and go west towards Manassas. Since there is more than one of you, you can use the commuter lane, so get all the way to the left. Stay in the HOV lane for about 8 miles, and go PAST the Manassas 234/Business exit. About a mile after that exit, work your way all the way over to the right and get off at the 234 Bypass exit. Once you are on this road, it is 4-lane divided highway that will take you all the way to Dumfries. It is about 20-25 miles, but it will be more or less 55-60 mph smooth-sailing the entire way.
When you get to I-95, I would skip getting on there to go south to Quantico because 95 south through there can be nasty nasty with traffic too. Just past 95, 234 will dead-end with Route 1. Go right/south on Route 1 and you will end up in Triangle/Quantico. A little slower than 95 due to lights and commercial areas, but probably better than 95 on a Tuesday night.
And yes, listen to WTOP.