Real doctors are using this project. A doc used to using a mechanical stethoscope with no noise whatsoever, is in for a big surprise if he hears noise from a noisy old opamp.
The low pass you have put on the front end of your revised circuit kills any noise specs that might show up. Noise is found in the higher frequency ranges. That is why many music noise cutting circuits employ low pass features. Many noise gates are high pass cut circuits and noise removal on analog bucket brigade delay lines are sharp cut low pass filters. High frequencies are easy to amplify. Low frequencies are not. You would have to highly amplify low frequencies to make them more noticable than the amplified sound signal.
Real Medical Doctors are using much more expensive equipment than this project......why would they bother with getting out a solder iron and making something like this? As far as I understand, Doctors spend their off-time playing golf. Not making op-amp circuits.
Oh, by the way....These circuits are for fun...the manufacturer of these parts does not allow for their use in medical equipment. You are supposed to purchase special ICs for this purpose. The manufacturer has a medical disclaimer on all their components except the ones which go through more rigorous testing and which are deemed as components worthy of medical use. If you see a doctor using one of these home made devices, he is violating some basic rules......run! He is not a qualified doctor.
MP