Tootles,
I googled this question, and think you are right that the FSDOs control of the initial CFI checkride is closer than the impression I got in Florida a couple of years ago. As I understand it, some FSDOs will do all initial checkrides, some will have 'special' DPEs they permit to do them. It seems that schools can no longer select the DPE, the FSDO does that if they chose to use a DPE.
It seems like a local school will have the best knowledge on local practices.
On another note, I didn't realise the CFI-I could also be your "initial" CFI qualification; it can
rgds
421C