I would definitely use the adventurecycling Southern Tier and Atlantic Coast routes. The easy of identifying camping and lodging alone is worth using the route. It will keep you in the warmest weather possible, but don't expect it to be balmy. You must be prepared to ride in temperatures at or below freezing. The days are very short, so you can't wait for it to warm up before starting out or you will be having very short days. Snow and ice is possible anywhere along the route that may hold you up for days.
For all these reasons I would start as soon as you can get away. After all the weather warnings, I would also say that you will have some fine warm days as well.
Heck, you are 22 and can take all the crazy conditions that come your way. Just be well prepared with lots of different clothes(including very warm and wind proof), a good sleeping bag and shelter that will take you down to 0 F. and you will have a real adventure!
Start to plan on what you will do with your gear in DC. Lodging is all taken. Your will have to be with your gear constantly if you don't have other arrangements. You may find a bike shop that will store your gear for the day.
http://www.adventurecycling.org/