Hey, since the real poster haven't commented anything, I think that the culprit is John and here's my 'deduction' haha
Well, since the hint is 'muses up 'alibi', it is likely that John, the only person with a seemingly solid alibi that did this. The reason that I suspect this is, why didn't John hear the footsteps that the third party he was talking to in the phone did? I'm assuming that he didn't hear the footsteps cause anyone would surely mention such suspicious thing to the police had they heard it. So here's my reasoning :
John might've slipped some kind of pill into the victim's dinner, everyone had the opportunity to do so after all. Then, he excused himself back to his room and called his friend. After the pill had finally started to take effect, he went to the victim's room. I'm just guessing but he might've asked to meet the victim beforehand so that he won't lock the door. They DO seem like having a lot of stuff to talk about ( pardon my grammar here). Then, he shot the victim with Mycroft's gun before quickly hurrying back to his room, not noticing the sounds of his footsteps, all while still on the phone with his friend... Their rooms are relatively close so I don't think he would've been catching his breath...
I DO admit that my 'reasoning' sounds a LOT impossible... I wish the poster will just post the answer soon.... Correct me if I'm wrong, though