The second OO works-like has been assembled and shipped! In 1-2 weeks I will receive it and, hopefully, get firmware-uploading working at last. So, what can I do in the meantime? Answer: redesign the entire right-hand side of my PCB!
Yup, I'm going to try and ditch the ESP8285 (and all the external components it requires).
The ESP32-PICO-D4 system-in-package IC is 7mm square. My board is 9mm tall. With all the routing, it just barely fits. But it fits! Admittedly, I had to do some sketchy routing where the thermal pad used to be, and I'm not sure it will work. See, here's what the datasheet specifies for the ESP32-PICO-D4 footprint...
...and here's what I did to it.
I have no idea if this is an acceptable design approach. If it isn't, then I think I have to continue using the ESP8285. However, if it works, it opens up a whole world of possibilities that the current OO design wouldn't achieve! That said, I probably won't pursue this further until I've got a functional ESP8285 prototype.
Please get in touch with me if you have experience with the ESP32-PICO-D4, or experience doing hacky routing underneath thermal pads!