Have crunched the numbers from Flight Aware to plot the height/distance of the aircraft. It's a bit vague but gives an idea of when the problem occurred and how he brought it down.
My esteemed colleague David Learmount tells me that the climb shape is intially steep as the pilot looks to gain altitude asap, it then drops off slightly to reduce noise, and then slows again as he tries to get more forward velocity at the costs of climb. Somewhere between this point and the next the problem occurs and he begins to descend.
About halfway through the descent there's a slight climb again and David feels this is probably because the pilot has at that point decided where he wants to ditch but has too much speed so he climbs to lose velocity before descending again into the Hudson.