i have 2 im not going to mount them but..
you could try to find long enough screws and mount them on the bottom of the case. drill holes on the base of the case aligned with the screws attaching the rubber feet to the brick. remove screws from rubber feet. use longer screws through the base of the case into the holes where the rubber feet screws were. I would keep the rubber feet on for vibration absorbtion. not sure if this will work but im guessing it will if the so called longer screws had the same threading as the screws which were used to keep the rubber feet on.

I'd start by getting a utility rack shelf. Then see if any of the pre-drilled holes line up to the feet of the Brick or mabe even faster with industrial velcro. It is heavy enough that you might need anyting that a shelf to set it on.

Rack-shelf + Zip-ties. Simple, effective & non-destructive.