the FAA will pretty much inevitably consider him/her to be PIC
There is no "pretty much" that I can see here. An instructor delivering instruction on board is ALWAYS the PiC.
The OP is doing himself no favours by allowing any suggestion otherwise.
I have been accused of infringing class A whilst instructing a qualified pilot (I didn't, but that is another story). Whilst I needed some supporting information from my student this was always about my command of the aircraft, and my licence.
G