How to fix a chair in 20 min using a Makerbot

I have this office chair that lost one of the bolts that holds the backing on the back support so that it keeps falling down. It's annoying so I can't lean back in my chair.

So I was thinking, "Hey (myself), I have a makerbot! I'll just design and print a new bolt to hold my chair backing together". I don't usually have conversations with myself but it was a lightbulb moment.

First, I took my calipers and started measuring the hole dimensions. Total bolt length would be 30mm (1.2"), abou