After installing the monitor and shelf in place, I made sure to get the computer up and running before putting the rest of the components inside.
After that was finished (and I played around for a while), the next step was making sure the motherboard and power supply fit properly. I placed the motherboard on one side (using PCB feet) and the hard drive on the other (using velcro) and tried installing the vertical shelf.
Unfortunately, my initial attempt didn't work - there wasn't enough room for the power supply and the frontx cables I was planning on using weren't long enough to reach to the back panel with the motherboard ports facing to the right. I ended up having to face the motherboard ports down towards the bottom and move the motherboard off center to the right to make room for the power supply.
I was worried initially that since the ports were facing down and the whole thing was off-center that the fan underneath wouldn't keep things cool but boy was I wrong. After leaving it on for at least 6 hours it was cool as the other side of the pillow in there.
Here is the power supply in place: