I was wondering if it would turn out that he had actually murdered someone in the past, and his conscience and/or psychosis was causing him to imagine his own victim in the window. I did not anticipate the actual twists at the end.

And judging solely by the bit that you tacked on to the end, the Robert Montgomery version sounds horrible, both in Montgomery’s performance and the extra added twist, which seems like one twist too many. (Maybe someone felt they had to show that he didn’t get away with it?)

As you point out, as an alibi it would immediately fall apart. Despite that, my impression was that we were meant to interpret it as one. (Your suggestion that it was just a performance makes more sense, but I’m not convinced that was Fletcher’s intent.)