Your most direct route is 1-87 to NJ Tpk to 1-95 to Wash DC and points south...true, it is busier but the only really important consideration is to remember from NY to Wash is only 4 hours (without traffic) and you just need to avoid a rush hour in this window...ie driving it from 10 am to 2 pm you'll be fine....or 8 pm to 12 midnite etc....
In fact, it's worth noting that you can completely by-pass Philly on this route, 1-95 thru Baltimore never really slows down much even at rush hour....your only big worry about traffic is Wash DC which I would be exceptionally careful of....use the Beltway and avoid weekday rush hour!
Also, if you take the I-81 route, you must worry about terrible lake effect snow (probably worse than Buffalo's but doesn't get the publicity!) which can hit bad anytime in winter and anywhere from Binghamton NY on up to the Cdn border (a 170 mile stretch), and of course can really slow you down and make for some very taxing time behind the wheel.
Good luck!