Ah okay. I was able to solve any while-plugged-into-usb issues with reboots. I did not see your last post here before continuing testing but yeah, I basically confirmed what you're saying:
F13-F24 keys work fine via USB using new experimental firmware.
F13-F24 keys do nothing via BT. (and I guess never will, due to the hardware limitation)
It would have been great to know this before purchasing, as it was a hard requirement to be able to send F13+ keys wirelessly. I would suggest making it clear somewhere in the documentation that F13 and up is not possible via BT. Tony, I understand if you only just found this out yourself about that RN42 module, as the need to use F13+ keys wirelessly is pretty niche and easily overlooked. Weirdos like me and sushi dragon are always looking for ways to send strange keycodes wirelessly with one hand, since all the usual keyboard inputs are typically mapped to some software that's running during our performance.
In any case, I guess I'll just use UCR (linked by Rilez, mvp, above) to remap some generic keys on the twiddler to F13 or perhaps even midi, to use in TouchDesigner directly.