From my experience with Raspberry pi, the pi will not work with PoE. But you can go the the link provided, if you have not already been there, and purchase this device and they claim you can do it.
https://www.raspberrypi.com/products/poe-hat/
Would be interesting to see if it will work. Brian probably has the answer. If you can, it looks like a new design will be needed. The big issue I see is how are you going to attach the HM board to the pi.