Regarding Mute Swans in Connecticut, I just have a few anecdotes from the seventies. I was in the Coast Guard in New London and often worked with the DEP (now DEEP) on pollution issues. Back then the DEP did addle Mute Swan eggs. They would not hatch, but the swans would keep brooding until they finally gave up. I am not sure if the DEEP still does it.
Even back then most people viewed the swans romantically. Once, when a boater ran into a Mute Swan and killed it, we got a few calls asking us to apprehend the boater. We explained that no law was broken and the Mute Swans were not protected. Now I live in New Haven County, but it does seem to me that the population at least in the western part of the state has stabilized. That is not necessarily a good thing, but they are large and quite territorial, so they may have reached a limit here. Maybe someone from the DEEP can shed some light.