The FAA will only be able to provide you with publicly available information about local CFIs or 141 pilot schools. They are not permitted to make any subjective comments about any instructor or school, only provide you with factual information that they have on file. Therefore, the information you may glean from a call to the FAA may be very limited.
Your second idea of calling a DPE would probably answer more of your questions, as he is not an FAA employee. You'll have to judge for yourself whether his opinion is valid and trustworthy.
Ray