So, on to your theory, @MrsJellybee . I can honestly say that this has never crossed my mind. I think it's brilliant, but I don't know that I can say I believe it. There are definitely some things that don't make sense in the way that the situation was presented to us. First, the sound of gunshots carry a long way. It would definitely have been heard by someone, especially at night. Even if all the officers were partying inside, I don't believe that an academy for wayward seaman would have no guards outside at all. So that's a point in favour of your theory. A gunshout should definitely have been investigated, but wasn't.
Where did the door guard go? Chauncey may have simply ordered him away. He's an admiral after all, but he must have been around somewhere while Stede was being abducted, but I can see why he wouldn't come looking - he already knew Stede was escaping that night.
But as for the rest of it, I really can't say that anything else gives me clues to support your idea. It's not that hard for Chauncey to repeat what we know is in Stede's own head, because it's the opinion he's had of Stede all his life. Stede has always been a 'nothing' to Chauncy and there is no way he would ever accept that Stede has anything positive going for him, so Stede's positive interactions with Ed that meant Ed gave up piracy can only be the result of some weird, un-human spell, because noone in their right mind could ever think enough of Stede to want to do that. Same with his dear brother Nigel; in Chauncey's mind, Nigel is so far above Stede that it's simply not possible for Stede to kill him honestly because Stede is simply not capable without some sort of demonic intervention. Stede's family of course are not ruined/defiled but freed; again, Chauncey would never see it that way. But it makes sense that Chauncey and Stede have the same thoughts because Chauncey is one of the people who has been feeding Stede those thoughts, all his life, until Stede fully believed it himself. And he has believed it for years. No wonder Stede is agreeing with him.
As for dying the same way - well, it was ridiculously impractical with Nigel and equally impractical with Chauncey. But we do see the rock he tripped on firmly buried in the ground so I think it's definitely possible.
And Chauncey isn't in nightclothes btw. He's in his uniform minus his jacket. The shirt (and waistcoat) he is wearing is the same one from on the ship when he was being Mr Wavy blade. I'd actually been studying the officers different uniform styles yesterday - thinking about how impractical his Admiral's one was with all those ruffles hanging down over his hands while waving his sword about. The other officers have a totally different style of shirt (and cuffs on their jacket). Yes, I am that sad for little details! So in my mind, Chauncey had been drinking heavily, removed his jacket and then gone out to find Stede. You can see in the pic that he's still dressed.
The last thing is it never being mentioned in S2. We know about the run time and the budget cuts so that is one explanation. But the bigger thing is that to Stede, killing Chauncey wasn't the reason he ran. There was no need to bring it up because it would have sounded like an excuse, and Stede isn't the type to make excuses. He has always run away from situations that make him uncomfortable or anxious and this is by far the most scared we have ever seen him. Running away was probably going to happen even without Chauncey. So to Stede, it wasn't relevant to mention it. In S2 he had recognised his S1 failings and is trying to make up for them. Telling Ed about Chauncey would cheapen what he was trying to do, which was to wholeheartedly apologise and win Ed back. He would never want it to sound like he was making excuses so not telling Ed makes perfect sense to me.
So, although your theory is a wonderful one, and definitely worthy of further consideration, you haven't convinced me yet! It's fascinating to think about though.
Blimey that was long!! Sorry 😅