Today, the enclosure and PoE switch arrived in the mail. So I assembled the tiny home cluster and confirmed that everything works, hardware-wise.
Components:

Yay, sweet LEDs.
It would have been cleaner to use the new Raspberry Pi PoE HAT, which will also add a bit of cooling to the Pis. But my local maker shop doesn’t have them in stock. So I ended up using the Adafruit PoE module and isolated them with pieces cut from toilet paper cores.
Each of the Pis posted, and booted Raspbian Stretch without problem. Part 2 will be playing with some cluster technologies. I want to pick up both Kubernetes and Spark, but will probably start with Spark.