The Mosquito wasn't smaller than the Beaufighter.
The Griffon wouldn't have been available in sufficient numbers, irrespective of whether it was to be used for other aircraft, when the Beaufighter II was produced.
The mosquito had less accessible and contiguous space for mounting radar equipment, it would require a greater effort to package the electronics. The internal space of the Beaufighter was perfect for mounting electronics which had not yet been carefully packaged and miniaturised. Such efforts require time.
At any rate the radar engineers remarked that they found it a convenient aircraft to work with.
There were only 300 Merlin Beaufighters produced so it might not have been too taxing to use the Griffon.
A Griffon Beaufighter might have addressed criticisms of the aircrafts limited speed.