So lots of people have asked me this...

It turns out in my diagram in the previous update that the microphone quality doesn't matter.   Here's why:

I play a sound x through the good speaker (G), record it with the shitty microphone (M).  I then do the same with the modified sound y and bad speaker (B), and analyse the difference.

Turns out I'm analysing:

M(G(x)) - M(B(y))

And since M is present in both terms, the eventual result after many repeats will be:

M(G(x)) ~= M(B(y))

G(x) ~= B(y)

So the microphone got cancelled out!   (Note this is only strictly true if function M is invertible, but we'll assume it approximately is...)