I wonder if you could cut open a circular hole (the size of the radiator), in the very top of the cabinet, for access? Maybe use a jigsaw or a router with a plunge bit? From in front, you couldn't see the hole, and the face of the cabinet, and the passive radiator slot, would still look stock. Then you could reseal the top of the cabinet, with a new board (maybe a nice hardwood panel) that could be attached to allow future removal for other maintenance, when needed.
Good luck!