I finally figured out configfs and got everything working on my Mini 510. I had to read several how-tos and the kernel documentation to understand it.
It just goes to show you can solve almost any problem with software!
I was able to mount the Zero in the drive bay by modifying the original hard drive carrier. I could have just stuck it down with foam tape, but this way I can remove the Zero by undoing one screw. Kind of handy if you need to change the SD card. Running the USB cable required only a bit of plastic trimming. I broke off part of the shell of one of the USB ports, stripped the cable end, and soldered it to the port. A blob of hot glue protects the connections. After the laptop was re-assembled I could hardly tell it was modified.
And there's enough room in the drive bay for any (small) project I'm working on!