Best part is, I don’t even need to confirm or deny whether or not Kinzo was dead at the time. I just have to ask: how’d he switch that letter then?
Check my second theory.
Jessica wasn’t dead when the group peered through the gap. She fired the gun as instructed (breaking the window), and simply waited for the group to free her. However, the rope was tied around her neck and the end of it was on the dark side of the room on the right, out of the group’s field of vision. The culprit, Genji, then opened window 2 from the outside (through the hole in the window) and pulled on the end of the rope, killing Jessica. He then cut the rope short and took it with him. He could accomplish this without ever entering the left half of the room, and thus wouldn’t have cast a shadow for Hideyoshi to see.
Could swear I mentioned somewhere the gunshot was a part, and a result, of the culprit’s plan… Oh, well. Now I’ll say it even in red. You’re not getting away by claiming it a simple stroke of luck.
I swear, you tell them they can’t handwave it away and they go and to this to me.
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Actually you never said it in red. So thanks. 
This sounds a lot like the theory Rune suggested earlier, but this one I’m having a lot harder time visualizing. What exactly would’ve been the threat for Jessica? Why would she not stand up and just… remove the rope from her neck? With Rune’s you had the excuse of the weight, but here you can’t have one - the window is closed. By extension then - why even fire the gun? You can claim it’s a prank but… what does the prank accomplish? If the point was to fire the gun, why the rope? If the point was to get attention, why didn’t she say something or scream? I have a hard time imagining why go through the bizarre effort.
More importantly, you can’t cut the rope to be as short as it actually ended up being if you did it from the window. You’d end up with pretty much the length of the entire thing.
Also, why wouldn’t have Jessica done something to fight back - since Genji would’ve been strangling her by pulling from the window?
It just… feels more like a theory to satisfy the reds a bit, doesn’t it?
Well, she’d fire the gun because of the threat on Natsuhi. And it’s possible she didn’t struggle because she passed out, possibly due to fear or the like. We could also say that the end of the rope was left on the north side of the room, such that Genji could pull/cut from there while still being on the right side of the door, out of the shadow casting range. Depending on how literal we want to be with Hideyoshi’s claim, too. It’s possible that the rope was left forming a line to the northwest corner of the room, and Genji snuck around the walls, avoiding casting a shadow, and pulling from the northwest corner blindspot. Seems possible to envision to me.
Stubborness is a method that won’t do you any good. Years ago I became mentally prepared through rigorous torture by the person that beta’d my gameboards.
In the end, you’ll only confirm what was obvious to begin with.
Firstly, I can’t help but point out that the notion that Jessica was fully conscious when firing the gun, but then conveniently passed out a second later, and that there were no signs or noticable changes to her body’s position to be seen as a tight rope pulled and choked the life out of her… seems a bit too much, even by my standards.
Secondly, let’s make this simple. Anyone on the left side of the room would’ve had their shadow cast, regardless of where on the left side they were. Let’s also make it so that the shadow would’ve been long and cast towards the right of the room. Simply put: it would’ve been seen by Hideyoshi. Of course, Hideyoshi would’ve been distracted and happened to look away for a few fleeting moments at a time at most. Not enough for Genji to cross over, cut the rope and set up the scene to his liking.
It’s good rope, y’know?
Food for thought…
The culprit is either:
-someone with an alibi for the murders
-someone without an alibi
-one of the victims themselves
-someone not even on the alibi radar (Kinzo, Kyrie, that guy from Rosa’s backstory, etc. literally any person that’s not even supposed to be around)
Mostly important cause… why even shoot the gun?
If you have no alibi anyway, there doesn’t seem to be any reason to do that.
Same if you’re a complete phantom.
Making people second-guess Natsuhi’s time of death didn’t really seem to accomplish much.
For the victims, Natsuhi couldn’t have moved the gun back.
Jessica could have fired it, but then things get kind of weird. (how did she strangle herself/break the window)
Meaning… people with alibi seem to be the only potential culprits with a decent enough reason to have that gun go off somewhere.
At least, unless there’s some reasoning that I’m not seeing, or the scheme for framing Krauss was so c o m p l e x that there are just weird parts like this. Of course, people with alibi are also the only ones that couldn’t possibly have fired the gun, so good times. 
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Same theory as above, except [color=blue]Jessica was poisoned, the effects of which look like asphyxiation. The rope was always at the length at which it was found, and it was just used to trick Jessica into thinking she had a chance at surviving if she shot the gun. She did so at the window, but by that point was already succumbing to the poison and couldn’t move her body, using the last of her strength to pull the trigger. She then succumbs to the poison, and Genji simply opened the window from the outside while getting the bolt cutters.[/color]
Well, wouldn’t that have been convenient. Being aware enough to listen to, understand, and follow through with shooting the gun, but at the same time being so out of it that there was a sensation of being choked. You have to wonder how in that woozy of a state she kept herself so perfectly still.
Oh, well.
[color=red]Jessica had not been poisoned or under the influence of any drugs that would’ve changed her perception of reality. This applies at the time before and the moment of her death.[/color]
[color=blue]They didn’t see Jessica but a fake body/fake legs dressed as Jessica. Jessica was put in a deathtrap just like in the intermission - but in a different room. Afterwards he rushed to where she was really kept and cut the rope she was dangling from. Then while getting the cutter he carried her into the VIP room through the window to the right, quickly pulled the legs away while Hideyoshi wasn’t looking, and threw Jessica down in its place.[/color] (alternatively he carefully slid her into place behind the fake legs, then quickly pulled them away. The suspicous bit wouldn’t take much more than a moment.)
And cause it’s so fun - [color=blue]A random other person X (or Kinzo-who-was-secretly-alive) was put into a deathtrap similar to Jessica’s. Rest is same except Genji only puts the gun into VIP room.[/color]
Yo some guy called Crooked Hinge called, he wants his shit back.
In all seriousness, let’s cut through all of this in one shot:
[color=red]When the gunshot occurred, the gun that caused it was inside of the VIP room.[/color]
The rest of the problems with this theory should come from there. And if the problems don’t become apparent with the murder, they will with the letter.
Just to confirm, does this red also extend to the possibility of [color=Blue]the culprit having placed the gun somewhere inside the VIP room where it could be easily reachable through the gap (such as by attaching it to the other side of the door with tape or somesuch), and covertly sticking their hand inside for a short moment to pull the trigger while pretending to help break down the door[/color]?
Hooray, I finally had the time to reread through the narrative and take some notes. There was some stuff I had glossed over before that is likely relevant and should be thought about, such as Kinzo’s suicide. Now I just have to find the time to go through the notes and properly process the information therein.
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Two words: fake body. 
Your assumption is correct, the red does indeed counter that possibility as well. Would be pretty cheap otherwise.
Well, in that case the main problem to tackle with this gameboard is abundantly clear indeed. Neither Shannon nor Genji could’ve shot the gun, but it seems nobody but those two could’ve swapped the letter. The gun can only be shot by a non-Shannon/Genji culprit, Jessica, or Natsuhi. Jessica dying from asphyxiation and being witnessed stationary on the floor right before the gunshot was heard makes it unlikely Jessica shot the gun. The gun being found beside Jessica’s body makes it unlikely Natsuhi shot the gun.
As the bedroom Natsuhi’s corpse was in was not described in any way, it would be strange if any detail about it was relevant to the answer, but I’ll throw this in anyway. [color=Blue]Genji had instructed Natsuhi to shoot herself, or else he will kill Jessica. A string was attached to the gun that either pulled the gun out of the room through an open window with a counterweight, or Genji simply ran fast enough to use the string himself to pull the gun away from the room before Krauss entered it. Or perhaps Krauss picking up the key that had a string attached to it triggered some kind of string trick to move the gun out of the room. In any case, Genji took the gun, entered the VIP room through the side window (perhaps he had set a yet another string trick he could use to smash the window from the inside by making a hammer crash into it or somesuch, allowing him to unlock the window and go inside), and threw the gun near Jessica’s corpse at some opportune moment. Then he rejoined everyone with the bolt cutters.[/color]
Shannon has her fingers in all the right pies, so she’d be in the best position to manipulate things to happen the way they did… but she couldn’t have shot the gun, and she was apparently in front of the VIP room door all the time. Without some seriously impressive automated mechanism, the crime seems impossible for her to have committed.
Naturally, the issue with that is:
A piece of advice:
Be careful not to slip into the territory of forming theories just for the sake of making it “work” with the reds. This not being directed at anyone specifically, but having seen some of the discord discussion, there were a lot of solutions proposed that would’ve “technically” worked with the red, but would’ve essentially been a slight variation on a theory that had been shot down before. My position from before hasn’t change - my objective here isn’t to “win”, it’s to have fun and have you reach that finish line. There’s no point if you’ve got 99% figured out but be denied victory because you didn’t give me that 1%.
(One could argue the importance of certain details is subjective, but I try to be as fair as I can about it. And in my opinion, I have been.)
That said, there were also a lot of points and questions brought up through the course of the game - some were good, some were pretty off-point, but I will commend you all for thinking over the details here. I know you’re stuck. As I said - this isn’t and was never meant to be easy or trivial.
But there is a path.
(Edit: This post ended the game. I figured I should spoiler it in case anyone reading this in the future still wanted to think about it before reading this.)
Original Post
Well I can’t not try this one.
[color=blue]Same initial premise as my previous one. The “legs” they saw weren’t Jessica’s. However, a mirror was placed diagonally in front of the gap - so the window they saw “across” was actually the window to the right. (Seeing how it was a small gap, so the mirror didn’t have to be that wide, so it’s not that unreasonable.)
This, of course, turns most of the room into a massive blind spot, and Jessica’s death trap was set up proper in the center. After the shot, Genji entered through window 1 (which is now out of view) and cleans up. After that, he waits for his chance when Hideyoshi was looking away and swiftly pulls the mirror away to the right, leaving them with an identical scene there. Then he opens window 2 and throws everything outside - the mirror crashes into thousands of shards. He breaks the window to make it seem like the shards are just from that. Then he returns with the cutter.[/color]
Edit: Actually nevermind. The image would have been the wrong way around for them. Should have slept on it…
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