The neighbor obviously doesn't intend to be, and isn't interested in being "neighborly" so I wouldn't waste anymore time trying to talk or reason... it'll only make things worse and give you ulcers. Any sort of "getting even", or "this'll teach 'em" attitude/actions won't make things better, and probably worse in the long run. It's time to take another route, and no matter what that route is it's most likely gonna' cost you some cash... it-is-what-it-is. A lawyer? Well maybe, but I'd start with city officials first... maybe the engineer, city attorney, mayor???
There ain't any sense in cutting off your nose to spite your face... even if it's what they want, my thinkin' is the only way to guaranty there won't be future problems is a privacy fence the full length of the adjoining properties. At least with a privacy fence you have something to show for your cash, and near 100% of neighbor problems are eliminated. When you get the permit you'll probably want to ask about the A/C unit, but I'm bettin' they'll tell you to see a lawyer. I know what I'd do, I'd cut one of the privacy panels to fit down over it and box-in my side of it, set a planter on top. I'd box it in tight so I won't get any air flow... I'm bettin' they move it within a year and then you can replace the panel with a full one. As far as the tree, run the fence up close to it and "box" around it on your side... I'm bettin' your wife can come up with some decorative stuff to hang on that part of it, maybe incorporate a little shed for the yard equipment... whatever.
Privacy fence... out'a sight, out'a mind... and that means "piece of mind" in this case.
Gawd I hate neighbors...