The answer to the problem actually came about thanks to an elderly lady who was walking along the beach. I was astonished to see this woman walk right past the scoters without them becoming alarmed. The secret was in her behavior, she wasn’t paying any attention to the ducks, and instead was focussed intently on the ground at her feet looking for something interesting that the tide had brought in overnight. She was also walking quite slowly. In general, I have found when trying to approach a wild animal, it is best to avoid making eye contact(eye contact labels you as a predator).
I decided to imitate her behavior, and gathering up my chair and tripod, I slowly walked down the beach, with my head hung down, looking only at the ground. Viola! Before I knew it , I was opposite the feeding birds. I still didn’t look directly at them and like a movie in slow motion, I set up my gear and began to photograph them!
The birds eventually tired of a location, and repeating the same pattern of a far off shore flock and string of swimming birds to shore, they would move further along the beach. Repeating the pattern as before, I was able to reposition myself without difficulty.