I wound up using the hardware that I built for this for my 8008 emulator, and I really didn't give this project any more thought. It seemed that the disk would fail randomly after loading a random number of sectors from MS-DOS.
In the meantime, I bought an ESP32-CAM with a bad camera (actually, I discovered that one of the camera voltages was missing). So, I ordered a few more ESP32-CAM's and chalked it up to experience. But, the CAM board has a nifty SPI pseudo-static RAM component (this version of the ESP32 has a 3.3 volt 8 meg PS-RAM). I wondered if it would be possible to connect it to the ESP8266 and use that for the 1 meg of storage needed for this project instead of the flash cache system, which is quite amazing, but still slow and brutal on the flash. I built another version of the hardware, removed the PS-RAM from the ESP-32 and connected it up to the SPI on the ESP8266 board. After some datasheet and ESP8266 SPI mystery solving, I got this working.
I'm testing the RAM now. The next steps, which might not happen for a while, would be to modify the original author's cache system to use PS-RAM and not the flash area of the ESP8266. it would be best to use it in "burst" mode, but, one step at a time!