Are you starting at the Bridge, at bridge level, or are you coming from the greenway? Honestly, if you are coming from NJ or are in the neighborhood at street level already, I would not go down to the greenway just for that stretch to Dyckman. Although not as initially pleasant, it might be worth considering going up Broadway (either all the way to the Broadway Bridge, or at least to Dyckman where you could go over to Seaman Avenue up to 218th, then back over to B'way as noglider indicated). You could then go into Van Courtland Park at 240th street and pick up the South County trail, OR, stay on Broadway into Yonkers and then get on the Croton Aqueduct path on in to Hastings. Most of the path is nice, however, early on there are some unpleasant curbs at cross streets to the path in Yonkers. It then becomes very scenic with views of the Hudson.

Broadway Bridge is a little tense with the traffic. There is a side path, but one is supposed to walk the bike when using it.

Obviously the choice is yours, but it sounds like you are covering substantial miles to Hastings on a heavy bike. I would think that between the extremely steep climb from the greenway at the GW bridge up to the last section leading to Dyckman and the hills in Inwood Hill Park, and steps, you might want to consider a slightly less scenic but more direct route through the Manhattan part of the trip.