At last! We have peace between the cats!
They still chase each other and wrestle some, but there's no more growling, huffing, hissing and/or full-on attacks. These behaviors were brought on by the sight of another cat outside and is called re-directed aggression.
It took six weeks to get back to normal. During that time we had to keep the cats physically separated, which meant keeping doors closed that are normally opened. That wasn't just inconvenient. It impeded the flow of air through the house, which affected the temperatures of various rooms.
To get them used to each other again, we had to open the door a little so they could see each other, and eventually referee by standing in between them with a spray bottle of water at the ready.
However, all is well now, and we're really, really hoping there isn't another sighting of the neighbor's cat any time soon.