Pretty much what you said. I asked a removal guy, and he said they are practically impossible to get rid off. They feed on live insects. So if you can keep your yard virtually pest free, then they will have no reason to be there. He told me to shoot them with a subsonic 22 and call the police and tell them you just dispatched a "Possum on the Half Shell" just to cover your backside.
I went 11 for 11 in 2016 with 90gr ballistic tip out of a .243 Winchester. Shots were from 10 feet to about 80 yards. Deader than a flat tax every time.