but it makes for heavier turning

For sure a good point. I guess I may need to make a pile of sod and clay near the bin and add it bit by bit throughout the spring/summer.

If you've already removed the soil, you can put it your compost.... but do you have some place else that needs some soil. When digging, I usually find someplace else in my yard that needs a bit of fill.

Composting the clay soil will lighten it up. I had clump of clay stuck in my bulb hole planter. I got frustrated, leaned it up against the shed, and then forgot about it. The clay turned rock hard and was cemented to the metal. I put the entire tool in the compost pile with the handle sticking out. A week later the clay was much lighter (and moist) and slid right out.

I think I would but I was under the impression that doing such would mean that the area would not be ready for planting for ...many months?

And if I did prepare the new garden as you describe then does one put (so much) soil on top of the cardboard so that when digging holes for the plants that one does not dig through the cardboard? If true then that would be a lot of soil?

Obviously if you plant immediately you might run to some of overturned sod, but it's easy enough to rebury as needed to smother it.

When i have thrown sod clumps (with clay dirt attached) into my compost, the worms just love it. After a few weeks when i go to turn the pile, there will be hundreds of worms swarming the sod/clay dirt. They appear to be standard earth worms vs the red wigglers though... which are through out the whole pile. I break them up when i turn and don't seem to have any issues of the pile cooling down noticeably.