It looks like Noel has it. According to the December 1944 Official Guide, the Murray Hill left Boston at 8.00 am, arriving GCT at 1.00 pm, and #41, the Knickerbocker, left at 2.00, arriving in Poughkeepsie at 3.45 pm. By coincidence, the B&A had an 8.00 am departure arriving in Albany at 1.15 pm, by which time the sailor could have been having a sandwich in GCT while waiting for 41. The West Shore still had service from Albany, but the first connection arrived in Highland at 5.25 pm, and the first available on the Hudson Division arrived in Poughkeepsie at 5.08 pm. There were two others earlier, but both were nonstop to Harmon. The last connection that night to Boston was the Owl (which carried a coach on Saturday nights); he could have left Poughkeepsie as late as 10.03 pm, with a 20-minute connection at GCT. I think there's a good chance that he was able to fiddle something at the Boston end so that he'd be covered as long as he got back sometime Sunday. As to the question of the ferry, there is a reference mark showing ferry service between Beacon and Newburgh, and a summer-only bus connection between Greendale and Catskill, with no mention of Poughkeepsie, so the ferry was apparently gone by 1944.
As to the Haverstraw service, I remember the last ferry from Cortlandt St. left while I was working in New York in 1959 and part of 1960; I think the 42nd St. ferry lasted a little longer.