I was offsetting the height by adding a fraction of the height-scaled tangent space camera vector into the UVs before going into the parallax function. Also note that the offset has to be included in the UVs that are added back to the raw offset after the custom node:
Here a value of 0 would represent no offset. A value of -1 would offset by one height value, meaning the POM would push up from the floor instead of down. -0.5 would make it a centered offset. You could probably put a constant subtract 1 in the material so the parameter could be in the 0-1 range.
Note that currently when doing this, if the camera actually goes below the virtual top of the box that this offset creates, there will be a strange upside down projection of the POM. I am not yet sure how to fix that without adding extra instructions. See if it shows up in your use case.