Its pointless trying to breadboard microvolt level stuff*. There's just too much noise pickup. A well designed and decoupled minimum stray wire matrix board layout in a screening can has a reasonable chance of working OK, so dig out an Altoids tin, some feedthrough caps for the power leads (but typically you solder Ground direct to the tin), and suitable bulkhead mount connectors to get the signal into the tin and out to the scope probe via a BNC adaptor or similar *without* using the probe's ground clip lead.
* unless its a narrow-band tuned circuit or low-pass filtered to near DC