If it were me, I would stay away from the Washington Beltway. Coming down the eastern shore should be more scenic than I-95 to Richmond, and I-64 to the Virginia Tidewater area. But that is just me.
Or go 1 way, and come back another to mix things up. If you decide on the Washington Beltway, avoid the rush hour "parking lot".
And if doing 1 way down, and another back, I think I would do the Beltway down......there always seems to be a backup at Hampton Roads going west on I-64. Also, avoid the Hampton Roads Tunnels on I-64.....again it seems to always be a backup. The tunnel on I-664 is much less used.
If you decide to do the I-95 to I-64 route in Virginia, I highly recommend using I-295 around Richmond. I-95 through Richmond can get hectic. Again, avoid the rush hours if possible, although I-295 is manageable even during those hours.
While telling you what to avoid, stay away from Friday afternoons, Saturday and Sunday mornings going to the Outer Banks from VA., and again Saturday afternoons and (especially) Sunday afternoons coming back into VA.
We did the Bridge Tunnel pulling our trailer last summer. Nothing to it, but I have pulled through the tunnels in Hampton Roads before. Gotta cut your propane off before starting the trek over the bay. I usually do that at the last expected rest stop before getting to the area.
My trailer is 9'10", so with the taller 5th wheel you might want to check out the Bridge Tunnel website. I can't think that it would be a problem, as truck cross all of the time, as most of those are 13'6".