One of our native birds, the weka, is a great egg-lover and seems to be able to carry eggs off.
Got any intelligent, vicious, omniverous birds from the rail family about?
Another one that will sometimes
roll eggs back to whatever hell-hole it came from is the stoat, and I wouldn't be surprised if its bigger cousins like weasles are keen too.
They will massacre a whole clutch of chicks, but generally leave adult birds alone.