Missed an obvious step
In Part II above, the author goes down the wrong path by continuing to work on the device while it's still upside down. After removing the five screws, flip the device right side up, then simply lift the cover off. It's a tight fit and there's not much clearance, but if you lift the cover straight up, you'll be fine. It goes without saying that you have to unplug the power cord from the back of the device.
With the cover off, it's easy to follow how the CD is going into the machine and being ejected. In my case, there was just enough friction during the loading process to prevent the device from pulling the CD into the caddy completely, but I found that if I tapped the CD as it went in, this overcame the friction.