I found two small time saves that the existing runs don't use:

1. On the beginning of the Third Day, click on the door to exit instead of talking to Stanley. You have to walk a little bit farther, but this skips Stanley's cleaning animation, so it saves about a second.

2. When you leave Leonard Shoulder's house, tell Father Roache to go ahead instead of leaving together. (He'll ask you the Shakespeare question before he leaves.) This is faster because 1) you can double-click the exit to leave a little bit faster and 2) you don't have to watch Roache walk off the next screen to the left.

The Roache thing is definitely a good catch, when I did my run I never really expected people to find so many genuine skips and optimizations like this but it's great to see.