Let’s write down some reasoning, then.
The gun used to kill Rudolf was in the gun room when the dinner ended, and the gun room door was locked. It is impossible to get the gun from the room without going inside, it is impossible to go inside without opening the door, it is impossible to open the door without unlocking it, and only the single gun room key Genji had can unlock the door. Genji never went into the gun room after dinner before next day. Genji had the key in his possession until he came to the kitchen at 10:30. All this is confirmed in red.
Since Rudolf was not killed by a trap or a remote mechanism of any kind, someone must’ve gone inside the gun room after dinner. As doing so requires the key, this was impossible before 10:30. The only way to get the key is to steal it from Genji, as it is confirmed in red that he never parted with the key from his own volition. However, as Genji was locking up the mansion sometime after midnight, the key was on his person. We can trust his word on this, because Genji can’t be the culprit as he never entered the gun room. The alibi descriptions for the groups are reliable and it was impossible for anyone to stealthily steal or return Genji’s key without being in Genji’s group as described in the narrative.
So, who are the people who were in Genji’s group? First, Gohda. However, it has been confirmed in red that Gohda did not steal the key from Genji, meaning Gohda is not the culprit. Second, Kanon. Kanon was briefly with Genji from 10:30 onwards, after which he left on his own. However, when Kanon left at that time, the key was on Genji. The next time Kanon joined Genji’s group was when he and Kumasawa reported to him about Kinzo at 11:40. Kanon could have stolen the key then, but since he never rejoined Genji before Genji locked the mansion, he has no opportunity to return the key. The narration would have mentioned all instances of leaving a group, so Kanon couldn’t have stolen the key at 10:30, stolen a gun, returned to the kitchen, returned the key, and then been sent by Genji to attend to other duties.
Kumasawa joined Genji at 11:40, but she remained in his group until the mansion was locked, meaning she had no opportunity to steal a gun. Shannon and Nanjo joined Genji’s group a bit before midnight, and then left together for the guest house, meaning they did not have a chance to return the key, either.
Nobody else is mentioned as having joined Genji’s group during the first day, so nobody else had the chance to steal the key. Thus, it seems like there is no opportunity for anyone to have committed this crime. Genji opening the door to the gun room for someone else and keeping quiet about it would label him an accomplice, and thus wouldn’t work.
Right now, I don’t see any way around the key theft issue. It could be that I have some detail wrong somewhere, or that I’m overlooking something major. In any case, now I really have to focus on other stuff, so I have to let this mystery be for a while. Perhaps when I return, things have become clear.