As a lover of dogs, I propose a new set of rules making Lampe Park a dog friendly park similar to Fuji Park in Carson City.
I think that arrangement would drive the geese away or at least make the park grounds uncomfortable for the geese. As a responsible dog owner, I would pick up the droppings after my dog, as I believe my fellow responsible dog owners also would.
The geese would move on to "greener" pastures, safe from the perceived dangers of canine predators. Problem solved and we could all be free to picnic etc enjoying the park.