Instrumentation Amps for AC signal measurement
Whatever you're doing here is necessarily going to have a very high gain. The AD620 is a reasonably low-noise amplifier with a ~1MHz GBW product. Here's what the gain vs. frequency looks like for different DC gains: 

 

The AD8221 has a similar GBW product that behaves better. 



If you are using high gain such as 1000 or 10000 you would expect to see the indicated roll-off in the Johnson-Nyquist noise at 20dB/decade. It should not affect your measurement at lower frequencies of the flicker noise, but you may have to adjust your excitation frequency to optimize the performance. The voltage and current noise corner frequencies of both those amplifiers are less than a few hundred Hz, so something 1KHz or lower might be a good choice. 

You can get a flatter response by not trying to get all the gain in a single stage- split the gain into multiple stages. 

In your modulated scheme you have to have bandwidth at the amplifier for the desired signal bandwidth plus the modulation frequency.