I'm so sorry you've lost your potential new babies. I don't know of geese taking eggs but I haven't been keeping them all that long really, although they can be a bit mean to chickens, I've caught them grabbing their feathers once or twice. Funnily enough my broody and her chicks and ducklings are in a house/run within the geese's area.
Could it have been other wildlife? People tell me of mink or stoats taking their chickens in very rural places. It's odd because when I have a broody hen on eggs she goes mental if anyone or anything comes near her. It would have to be something quite bad for her to leave the nest altogether.
I too had a case of missing eggs, I had placed dummy ones in a couple of places to try and get the girls to lay where I wanted not where they did. The eggs weren't wooden or china, they were real ones which I blew the liquid out of (like you do at easter) and I filled with expanding foam filler!
Anyway one night they all disappeared, like you no shell or mess anywhere, I expected to find them half eaten and spat out somewhere nearby.
Foxes can get into the outer run area at night so it might have been them but there are occasional rat sightings as well, we live by a river.
It's strange though because I have found piles of eggs in various places well away from the run, hence the false ones, so they obviously were missed by whoever pinched those eggs.
I hope you get to the bottom of it for your own peace of mind, I'm seriously contemplating CCTV to see what goes on when my back is turned.
Best wishes, Helen