No study, however, links Canada geese to any infectious disease that is transmittable to humans or domestic animals.

The above statements appear to be in conflict. 

A significant amount of dog fecal matter did show up in our recent PCR water tests, as well as human DNA, which caused all the ruckus.

The Anglers Club was advised a few years ago that Goose Poop was NOT a significant contributor to pond water quality. Dog poop is of a different chemical make up. The problem we had, prior to the cull, was the children attending the Teach a Kid to Fish and Kids Fishing Contest events stepping in what had become a disgusting amount of Goose poop. It also affected the Veterans memorial. The average goose produces 1lb of poop per day.  If they bake in the sun, they actually turn into little straw like poofs.  More like straw like "poops". 

According to our documents, the idea that slaughtered geese will be fed to humans or animals is a myth.

You obviously need to check your documents again. The problems with "agendas" is they often either omit or twist facts if it helps their cause.  The biggest problem with donating killed Geese to a homeless shelter is more the problem of plucking them. No one wants to do it. Here is an article from 2019  about Salisbury and Ocean Pines euthanisia of [ Geese. ]

Over the years I have watched the failure of dog cutouts, guy hired with dog in kayak, high grass and most recently proposed special grass geese won't eat. May be but it is one thing to use this extremely  expensive solution in an airport where lives and millions of dollars of equipment are at stake if geese are sucked into jet intake and planting around our ponds.  Apparently that has been discovered which is why it was cancelled. 

It is unethical to kill an animal because it poops and we find it inconvenient when there are a lot of non-lethal management practices that can be employed.

I suspect you would be against all hunting of deer, geese etc. and I respect your opinion but please realize it is not shared by everyone and it is important to be sure that facts are not manipulated to push an agenda.