I always go 64 mph in a 55 zone, as in the rare event that you're pulled over at that speed, you'll only get 1 point on your license (10-19 mph over the limit is 2 points). Don't go 75 unless you want to get a "reckless driving" ticket with a mandatory court appearance ("reckless" in VA is 20 mph or more over the posted limit or over 80 mph regardless of the limit.)

Since you'll be a big group, it'll be easier and possibly cheaper just to drive all the way into DC and park at meters or pay lots, as others have said. It's very true that for 2 or more people, the Toll Road/66 commute is faster before 9:30 a.m. than it is right after. HOV lanes work wonders in Northern Virginia!