Based on the epic ******* nature of the neighbor and legal advice from the thread that I'm pretty sure has no actual attorneys, I'm going to change my advice for course of action. To hell with paying to have it cut down on his behalf.
Watch the weather, wait until he leaves, and stick your Stihl through the fence picket and cut a Kerf on the north side of the tree. Wait for the next norther...problem solved.
Oh...make sure you're solid on cardinal directions, physics, error probabilities, and of course where you home lies in relation to the above.
On a serious note, as a person that cuts tens of trees down and up on my property annually, I can say you don't need a ****ing forestry degree to figure out that PINE is a danger when dead. That tree is a danger and I'd try again for a certified letter so that I could promptly get paid when it falls on my **** or kills someone. Pine is a trash tree. It's weak and brittle when alive and it rots fast. Tell your dip**** neighbor that pressure treated pine doesn't grow naturally. He's a deadbeat bum and If I'm on a jury, the op is getting paid to whatever extent I can squeeze from cousin eddy over there.
It's worse than a pool. It's more like a time bomb with an iffy fuse. But, Like a pool that has fences and locks to mitigate risk, that tree needs to go.