First of all, lets look at some plants that might fill the bill from our Native Plant Database . Scroll down to the Combination Search Box and make the following selections: select Pennsylvania under state, herbs under Habit, and Perennial under Duration. Check Shade under Light requirement, and Moist under Soil Moisture. Click on the Submit combination Search button, and you will get a list of 45 native plants meeting these criteria that grow in Pennsylvania. Clicking on the scientific name of each plant will bring up its NPIN page which contains a description of the plant, growth requirements and and characteristics as well as images.
Mr. Smarty Plants is wondering about the size of the pond, and whether these are domesticated waterfowl (ie.pets) or free-loading transients? As you’ve discovered. ducks and geese are herbivores (they eat plants), and may well eat any thing you plant. This article “What do Ducks Eat?” gives us some insight into their dinning habits.
Is removal an option? This article from Penn State University Extension tells about strategies for controlling nuisance water fowl.