Well, that design didn't last long.
I bought a really tiny flash drive and loaded Pixel_x86 on it. It worked really well with the HP Mini. Pixel_x86 also has a persistent mode that stores changes to the USB drive if you boot from one, and works really well. So I decided the hard drive was redundant, and removed it to save weight. Thus, I was faced with a rather large cavity where the drive had been:
Then it hit me - why not put a Pi Zero there? I could run a cable inside the laptop from the Zero to one of the USB ports. I could then access the Pi via USB gadget mode, and everything would be internal and protected.
My objections (see previous log) to using gadget mode to access a Pi were nullified. So the portable WiFi Pi is no more. And the project just got a lot simpler and less expensive.