Now I need to make a fixture plate that mounts on my lathe's spindle, to do that I will use the back plate with D1-4 cam lock studs from my 3-jaw chuck!
I found a nice block of aluminum in my scrap pile, and machined one surface flat and counter-bored it to fit snuggly on the backplate. Then I transferred the three holes from the backplate to the aluminum block, and drilled & tapped them for 1/4-20 UNC around 3/4" deep.
After fastening the block to the faceplate and to the lathe's spindle, I turned the OD and face true. Then I removed the block from the faceplate, and put it in my Mill's vise, I had to remove one of the jaws to get it to fit!
Then with a 1/2" 2-flute end mill, I machined a square pocket in the center of the block around 1/8" deep. In order for the cubes to fit in this nest, I had to go and extra 1/4" past each corner with the end mill.
Now the cubes fit snuggly in the center of the block!