The OP says, “…the backyard has been cat proofed in that three legged cats cannot escape- and while not impossible, it is unlikely a stray cat could get in.” (bolding mine)
Simply, the noise the other night sounded like a cat fight. Dogs can’t access the backyard so that could be ruled out.
The fences here are all six feet tall and made of sheets that look like corrugated asbestos. The back yard is entirely enclosed with this apart from a side gate that abuts the house. It is about 8 feet tall and heavily latticed. The entire backyard is like a large cat run albeit with no roof. An athletic cat could get in or out I guess although I have never seen one in here since it was sealed.
Was your cat vocalizing both sides of the fight? 
He’s a very talented cat I’ll have you know. 
Now that I’m thinking about it, I’ve never seen one of my cats give any indication of dreaming. My dog does it all the time…paws twitching, muffled barks, etc.
Never seen one of my cats do it.
Some of my cats seem to dream, and others seem to give every appearance of being dead to the world. My husband’s male cat, for instance, mutters, mumbles, and grumbles in his sleep, although he’s fairly quiet when he’s awake. He twitches in his sleep, his eyelids flutter, and sometimes he wakes up with a jerk. Clearly, Charlie leads an active dream life.
As for the phrase Composure Grooming, I’m fairly sure that I read it somewhere before I ever got online. Feel free to use it, though.
My cat twitches in his sleep on the odd occasion.
Maybe you have unimaginative cats. Mine appears to dream nearly every time it sleeps. Of course, she doesn’t make a production of Cats! out of it.
I’ve never had a cat that didn’t dream. Maybe they’re not as active of sleepers as dogs are, but mine definitely dream.
Most of mine seem to dream now and then, normally it’s pretty subtle though. One like to spoon with me, and sleeps with his head under my chin. He must have been having a very bad dream the other day because he went from the normal little dream-twitchies, to muttering (he’s very vocal anyway) to growling & making Exorcist noises :eek: I decided at that point to remove my face from the vicinity, and he woke up looking very confused.