Quite a deafening silence on this post. If this is "faster response than Email" I can't say I've gained much.
Anyway, I've found out that one can't use a bridge rectifier to convert AC mV signals to DC because there isn't enough voltage to turn on the silicon diodes in the rectifier, which require about 700 mV to start conducting. Maybe I was just reading noise.
I have constructed a precision rectifier that will convert AC mV signals to a DC voltage using an Analog Devices AD736 RMS-to-DC Converter, under $8. A few capacitors for filtering finish the job. The details are in the AD datasheet for the device, available on the Web. It seems to work well but I still have a zero offset; haven't yet figured out where it's coming from and how to fix it but it's not so important right now, since I can definitely see and record the changes in current with the ADC16.