Yikes! 5:30 traffic on a Friday in DC! If I were you I would definitely take 301 through MD and avoid DC traffic all together. Like others have said, you'll end up below Fredericksburg in VA and probably will be faster. However, sometimes the traffic lights can back things up in the Waldorf area on 301. Also, don't worry about taking 295 around Richmond. I grew up there and have never thought it was a shortcut. Just take 95 straight through.
Iif you do want to do 95 in VA and not take 301, have you thought about taking the BW Parkway down? That turns into DC295 which will dump you on just a short segment of 495 before merging onto 95 at Springfield. I would definitely recommend this as opposed to taking 495 the entire way around Washington. You'd spend most of your travel time sitting on the beltway!
I'll be on 95 Friday afternoon with you on my way to Richmond! Let's hope it's a good traffic day! Although, I have to take 95 the whole way down (no 301 for me!)