I would say you need to abandon the idea of doing this "on the cheap" with a passive setup.
Even though you seem to class diodes as active components, I don't know of any that will conduct this low - let alone what you are going to do with the signal once you have removed the diode "voltage". Chances are anything that will is gonna be mil-spec and/or hideously expensive/unobtainable. Germanium stuff can come down as low as 180mv but this is still way over what you are after.
google "precision rectifier" there's plenty out there and depending on the opamp, they can work in this formation (i.e as a rectifier) down to a few micro-volts (some even lower)
the first thing that came up for me here was
which gives a nice precision full wave rectifier circuit which you could construct for
look at this mine first upper schematics (slide C); it is a 70Khz IF amp for measuring signal strenght. (for TDA7000 IC)
Last half of the schematic- passive part at the end: The right last 2 resistors provide current biasing two germanium point glass demodulator type diodes to the knee of conducting signal .. So, you can measure from few mV & up to 2V RMS signals..