Well, my roommate's parents had a similar problem with some new neighbors. they have a little ditch/rut thing(forget the technicalo name for it) that acts as the property line. With their pervious neighbor they had allowed them to extend their fence into their property so they could give their dog more room. When they left, the fence was still set up.
So the new neighbors took it upon themselves to assume that the fence was the property line. The stapled wireless fencing wire to the fence on my friend's side of the property line. His father went to them and explained the situation, but they refused to see his point. He left and returned with a copy of the surveyer's chart (also forget technical name) that showed exactly where the property lilne was and asked them to remove the wire and build their own fence on their side of the rut. The man refused, saying that they had just paid a lot of money to rebuild this fence.
So my friend's dad thanked them for fixing his fence, ripped the wire off of said fence, and later returned with a chainsaw and cut the section of fence that ran over the property line.
And there wasn't a thing the man could do about it.
So if your neighbor doesn't want to move the tree and he refuses to trim it, your have every right to cut everything on your side of the line, smile, and wish him good day.