This isn't solvable. Each loudspeaker and microphone has its own frequency response and will always measure the product of any two of them. This does not result

This isn't solvable. Each loudspeaker and microphone has its own frequency response and will always measure the product of any two of them. This does not result in a unique solution for any single frequency response, even when you know the clean source signal. There is always a degree of freedom of how much each device in a pairing contributes to the final response.