The trick was that the boxes had really deteriorated and the neighbor's trees' roots had found their way in through the rotted out bottoms. But we wanted to recycle as much as we could, so we gently slid them over and stacked them:
We found a few odd critters, including a blue snail (no picture...) and a salamander (or is that a skink?) and TON of huge pill bugs:
Then we cut the old squirrel cage in half and put that on there. Oh, and we had to dig out a ton of tree roots that had grown up between the cement slabs. The old 2x4 spacers between the slabs had rotted away almost entirely.
Next we'll build a new, slightly different shaped box where the old ones were and also one over to the right of the "new" one. After that, we'll move the compost pile to roughly where that hay pile is now, and then build a "hay cozy" over where the compost was. I'm sure it makes sense, somehow.