That is a tough question since compost is so valuable - soil structure or nutrients? Can you loosen up the top 6" to 8" of your clay with a pitchfork or shovel? Not necessarily digging and turning over but loosening (less work). Then I would put the compost on top like your other beds. Clay is really tough to loosen up with compost because compost would continue to break down. There are probably lots of nutrients in your clay but hard for plants to access.
