If you're actually going to Sanford, then it's no where near DC. You have to travel through Delaware and go down the peninsula to the eastern shore of Chesapeake Bay. If that's the case, you're going to have to travel through most of New Jersey to get there.
For the northern most part of the journey, I've always used the Mass turnpike, to I-84, to I-91 and then the Merritt (Route 15) to I-287 across the Tappanzee, then down the Garden State Parkway to I-95. Once you get into southern NJ, you can get on I-295 that parallels the NJ Turnpike and follow it to the bridge into Delaware. No toll on that road and the last time I was on it a couple of years ago, there was very little traffic.
If you aren't going to Sanford, but are going to Stafford, VA, then you should take a more westerly route. It's south of DC, right on I-95, but you can take the Mass Turnpike to I-84 and follow that across the Hudson in Newburgh. From there, you can continue west on I-84 to the Scranton area and then pick up I-81 south. Once you get into VA, you can work your way east to Stafford. That's more miles, but keeps you out of New York City and more importantly, you don't go through and inch of New Jersey. That's important if you are transporting any firearms, less so if you aren't. I drove to Texas last year with my daughter (and a couple of firearms). I opted to take that route instead of anything that would put me in New Jersey.
There are two major choke points on the I-95 route from Boston to NYC. First is in New Haven where I-95 and I-91 meet. They have been rebuilding that interchange area since at least 2005. The last time I was down there, which was about a year ago, it still wasn't done. Major back ups in all directions. The GW is always a crap shoot. I've taken it, but only very early on Sunday mornings. NYPD will close the bridge for any serious accident and the exits dump you into areas where you might not want to be and then you have to navigate your way across the river.
That's just been my experience, this is a case where YMMV literally.
BTW, if you have a ME permit, it's valid in Delaware. PA will recognize a NH non resident permit, VA will not recognize any New England state permits. I don't think VA requires a permit for possession, just for concealed carry.
And of course, once you get to FL you'll want a CCW permit.