After trying this, I'm not sure if it's beatable. The really annoying part is the drawer animation consumes so much of your time, and you won't know the next item until after that animation is finished.
I also found the controls slightly weird. Mostly when you're using the mouse button to pick up items and then space to place them. I would think the mouse button could pull double duty in that regard.
Over all, a fun and unique experience.