Our trip to the fort is about 875 miles one way. I have never tried to make the run non stop and always split the trip into two days. How far we make it depends on traffic and stops mostly. I can only handle about 12-13 hours on the road and after that I am pretty much wiped out. Rather then risk fatigue and not to mention just needing to be out of the truck for the night we stop. Now that can be as little as 500 miles for the day, or as much as 600 miles for the day. We start early enough usually on Friday or Saturday to miss the DC traffic, Around 7:30-8:30am. Richmond traffic has never been an issue for us since we hit the area outside commuting time. We usually end up stopping at Point South KOA (I95S Exit 33 in SC), though one rainy day south we only made it to New Green Acres RV Park (I95S Exit 53 in SC) and then had a year where great time was made and got as far south as Savannah South KOA (I95S exit 87 in GA). Usually we are stopping between 7-9pm at those locations, and since we are traveling with a caravan of campers it means we all need to be willing to go the distance.
But from that stopping point is about a 6 hour haul to Disney for us. That includes usually one fuel stop in GA and one potty break before the I4 exit. If I had to tack on the extra mileage I would try to find a way to still do it in two days time, but you are still talking about 23 hours on the road for the entire trip south. First I would try to get off LI before the traffic picked up. Even if it meant leaving at night just to get a few hours outside the area, then shoot down. Stopping points would still need to be figured out for you, do you plan to do I95 and deal with the tolls, or head through PA and avoid the tolls Mid Atlantic traffic.