I knew that I couldn't go on Monday in any case so I decided to wait and see if the bird was seen that day before I committed to the drive. I monitored the list-serves all day on Monday but saw no reports. In the end, I broke down in the evening and called Gerry Smith (a local birder) who confirmed that the bird was sticking but that it wasn't always easy to see.
So at 4:15am on Tuesday, I jumped in the car and drove the 6 hours up to Clayton, New York (the last exit before the Canadian Border and closer to Kingston, Ontario than any significant population center in New York).
When I arrived at the site I checked the marina and then did a thorough search of all the docks and hidden corners in the inlet, but came up empty. Gerry had told me I might have to wait the bird out so I headed back to the car to find a spot to settle in for a long wait. As I came back through the marina, a guy in overalls came out of the marina buildings and asked if I was "looking for the duck" (I though he was going to tell me to move my car). A quick chat and he'd given me a couple of other places to look so I got back in the car and headed out to a spot where I could scan the nearby shore of the St. Lawrence River. Within seconds, I spotted a group of loafing mallards on the shore across the inlet and there, sitting among them, was the Whistling-Duck (NYS 2012 #330).