I randomly decided to give speedrunning this a go, it was lots of fun and as I'm typing this my best time is 1:44.43
Time starts when you click play and end when the final dialogue starts, if you want to give it a try.
I had the same idea. I tried making a speedrun.com entry for the game but my account is not 7 days old :(. If someone else could create it that would be great. I'm thinking it should have 3 runs, this, Box% (Must reach last dialogue with all 4 boxes), and Void% (Ends when you fall into the void). I would really appreciate it if someone could add this to speedrun.com!