Coyotes (or fox) would probably help with the goose issue - but create some others of their own. Since there are so many coyotes can they be considered invasive or are they just reclaiming their prior territory? Fox?
Rob, Give me the skinny on this evasive business so I understand. Are they only invasive if they were never native and accidentally, or otherwise, introduced from another ecosystem?
We had a deal with VAFWS that they would give us all the grey foxes and Oceana all the red foxes they picked up in Tidewater for release on our installations. You've never heard squawking until you've heard a fox get a goose by its neck! The foxes had sense enough to stay off the runways.
Some species like the nutria were introduced from South America for trapping. They're destroying the levees at Mackeys Island NWRA.
Something like wolves or coyotes that may have at one time lived here? Don't know, but the game people don't have problems with you shooting coyotes . They weren't introduced, they migrated.
Even piping plover weren't local to the area until 20-30 years ago. A few straggled in, and the birders have gone berserk making them feel welcome.
The house finches aren't local either. They're native to California. Some pet store owner on Long Island was selling them as Hollywood Finches before WWII. When he found out that was illegal, he released them. They quickly spread along the east coast, and eventually joined up with the western population, and now cover the US. Probably not considered invasive.
The Eurasian Collared Dove was accidently introduced to the Bahamas in the '70's. A hurricaine blew them into FL in the early '80's. Now they cover the continental US, except parts of New England. Definitely invasive. Some states have no limit on them. You have to study their flight pattern vs the mourning dove, or you're going over your limit.
Kill starling and English sparrows to your hearts delight. They're not protected in any fashion.
Kudzu was someone's good idea to stabilize road embankments in Georga.
Lots of interesting stories, most of them disaster stories..... Google the topic. You'll be amazed.