The best thing about the game is sensing a distraction coming and bracing yourself in anticipation. You could try gamifying it even more and turning it into a kind of psychological resource management game, but I have no idea if that would actually be more fun. A really simple example would just be having a deadline and tracking the time throughout the game.
It's also fairly low-stakes, which gives it a lighter tone. I wonder how it would feel with significant implied consequences for not finishing that night? I imagine the emotions would be heightened and self-loathing would kick in, really highlighting the absurdity of the human brain's tendency towards procrastination at its own expense. My experience with procrastination has often involved real despair, which contrasts with the sheer pride and accomplishment of actually getting work done.
As it stands it's a short, sweet and relatable experience where the choices feel meaningful, and that's a success in my book.