That is some crazy heavy looking clay, Mark. I can't even begin to imagine how heavy it was to dig out. It reminds me of the mud-blocks that my African friends built their houses out of when I lived in Africa 30 years ago. But for them, they would have to mold them in a 4-sided mold and carefully extract them. In your case, it looks like you could just cut them to size with your spade and immediately start to build a house with them.
I also have clay, so my solution has been twofold. First, I mulch like crazy several times a year with a huge load of wood chips from a local tree trimmer. I get upwards of 20 cubic yards of wood chips per load, and I'll put those chips down everywhere -- up to a foot deep in places where I'm not currently gardening. The orchard gets a new layer of chips at least twice a year. All that carbon quickly breaks down, and he worm life in the soil is amazing. As worms and other biota thrive in the interface where the chips meet the clay below, they integrate the carbon down into the soil profile. I don't dig anything in, but let the microbes, fungi and biota do he work for me.
Second, I've gone to raised hugel beds --- a hybrid raised bed with a sub-soil layer of logs and such like you are creating. For the uninitiated, they just see normal raised beds. But what they don't see is a foot below the soil surface, all those logs and sticks breaking down.
I'm not a fan of the sloping sides of a hugelkultur for planting many crops, so I used timber frames to keep the soil flat/level. I get the best of all worlds: the carbon and fungi from the buried wood, and the ease and improved soil from the raised bed. If your hugel doesn't work out as you wish, you can always simply go back and build sides around it and turn it into a raised bed easily enough. My compost seems to go a lot further this way, because it doesn't fall down the side of the mound, but rather, stays in place.
Please continue to post pictures. This is a fantastic project. Best of luck.