I really like this spin on the theme haha!
I'm not sure about the time constraints. It evokes a sense of urgency and I didn't fell like I had time to really read into the testimonys and deduce. When I read the first thing that sounded contradicting to another I convicted and happened to be right. Never figured out who the forgetful one was tho.
[spoiler warning ahead]
I also think the murderer was a little too obvious with them saying. I was in the library, bur never went close to the study. It makes them really stick out from the rest. Everyone else mentions where they have been, not where they have not been. I think it would help to figure out another place for him to be at that time that he lies about or making more people mention where they definietly didn't go.
Overall I think it's a fun Idea for a game