UPDATE, and good news for those interested. I rode east, from New Paltz, crossed over the Walkway and it does indeed connect to Dutchess Rail Trail ("DRT). By coincidence, I met a Walkway official on the DRT -- he was cycling over to the Grand Opening of the bridge over Route 55.
I didn't know how close I was to that bridge at the time, but I turned around just shy of a mile from there. So apparently that bridge connector is now open and it should be smooth sailing.
Incidentally, if you take the route that I did (eastward), bear left after you cross the Walkway. I followed a path to the right that appeared to be the trail's continuation, but it was an exit ramp. It was a very short detour, so not a big deal in any event.