Nice build, and interesting post. Have you tried to filter the 50Hz? It looks like you have plenty of signal, so it is not necessary. I am interested as using battery power, and still getting noise from the utility implies you may need more than a Faraday Cage ...or a really big one you can walk into. If you just shield the circuit, you will still have your body and the external wires picking up the noise.

It looks like you are already using differential inputs and have plenty of common mode rejection. I have seen some odd cases where single ended worked better, but if the energy is induced, as it appears to be, I would think the way you have it is best. At any rate, as mentioned your signal to noise looks nice, so keep on experimenting.

It has been a while but I have done experiments requiring a Faraday cage big enough to walk into and perform experiments without any external noise :-) --3D