With the exception of the Nulhegan (which likely will have no water in it and be impassable)and the Connecticut - and, of course, Lake Champlain - nearly everything between New York and Maine is going to be upstream work. With a lot of fast water. Fast, shallow water with no good bite for your paddle. You could have a tough time of it. If you're looking to do a trip like this in late summer, I would recommend a segment with a lot of lake and flatwater. Like, Old Forge to Plattsburgh (although low water will definitely be an issue on the Saranac). Or Moosehead Lake to as far as you want to go, even to the end at Fort Kent. Anything in between could be pretty miserable with a lot of heat & humidity and no water.
2-3 Canoe/Kayak Trailer